This postmortem report will provide all readers with important information about the Open Science workshop which took place in Vienna, Austria on the 20th of September 2017. The workshop was organised by the Open Innovation in Science Research and Competence Center, Open Access Austria, Austrian Transition to Open Access and Open Knowledge Austria. All authors of this document participated at this Open Science workshop and contributed to the report in a collaborative writing effort. In this report, readers will find an overview about the Open Science Workshop structure, presented content of the workshop, all slides pictures, social media interactions and everything we have learned from organising this highly important workshop on Open Science.

* All authors contributed equally.After the conference We Scientists Shape Science organized by the Swiss Academy of Sciences in Bern in January, 2017, several participants of the Scientific Careers workshop came together to present what we found were highly relevant points of discussion, including concrete proposals for action.  

This is a preprint journal club review of Cortical Representations of Speech in a Multi-talker Auditory Scene by Krishna C Puvvada, Jonathan Z Simon. The preprint was originally posted on bioRxiv on April 10, 2017 (DOI: https://doi.org/10.1101/124750). The authors have responded to this review, and you can find the comments on bioRxiv. The article is now published in The Journal of Neuroscience (DOI: 10.1523/JNEUROSCI.0938-17.2017).  

Published in "Latitudinal Controls on Stratigraphic Models and Sedimentary Concepts", SEPM Special Publication 108, September 2017, DOI: 10.2110/sepmsp.108.02. Accompanying data and code available at https://github.com/zsylvester/channel_sinuosities.Abstract Using a script that automatically calculates sinuosity and radius of curvature for multiple bends on sinuous channel centerlines, we have assembled a new data set that allows us to reevaluate the relationship between latitude and submarine channel sinuosity. Sinuosity measurements on hundreds of channel bends from nine modern systems suggest that there is no statistically significant relationship between latitudinal position and channel sinuosity. In addition, for the vast majority of submarine channels on Earth, using flow velocities that are needed to transport the coarse-grained sediment found in channel thalwegs, estimates of the curvature-based Rossby number are significantly larger than unity. In contrast, low flow velocities that characterize the upper parts of turbidity currents in submarine channels located at high latitudes can easily result in Rossby numbers of less than one; this is the reason why levee deposits are often highly asymmetric in such channels. However, even in channels with asymmetric levees, the sinuosity of the thalweg is often obvious and must have developed as the result of an instability driven by the centrifugal force. Analysis of a simple centerline-evolution model shows that the increase in channel curvature precedes the increase in sinuosity and that low sinuosities are already associated with large curvatures. This suggests that the Coriolis effect is unlikely to be responsible for the low sinuosities observed in certain systems.Keywordssubmarine channels, Coriolis force, sinuosity, curvatureIntroduction Submarine channels are common—and often beautifully sinuous— geomorphic features of the Earth’s seafloor that serve as important conduits of sediment transport from rivers and shallow water to the continental slope and basin floor. In addition to their role in the large- scale redistribution of clastic sediment, they often correspond to locations of thick and relatively coarse-grained accumulations that can host commercially significant hydrocarbon reservoirs. Ever since it was recognized that these features exist \citep{Henry_W_Menard_Jr_2__1955} and that their planform patterns can be remarkably similar to the meandering shapes familiar from rivers \citep{Damuth_1983,Clark_1992} the assumption has been that the relevant physical processes are fundamentally the same across the globe and, therefore, there is no need for facies and architecture models of submarine channels that are specific for different latitudes.  This line of thinking has been challenged by \citet{Peakall_2011}, who have looked at the relationship between submarine channel sinuosity and latitude and suggested that channels closer to the poles had lower peak sinuosities. They concluded that this is largely due to the Coriolis force having a stronger influence at high latitudes. Experimental work relying on a rotating flume tank showed that at low Rossby numbers (that is, when the Coriolis force is larger than the centrifugal force) turbidity currents do behave differently from the conventional model \citep{Cossu_2010,Cossu_2010a,Cossu_2012}. Building on these and similar experimental results, \citet{Cossu_2015} proposed that channel systems of the Cretaceous Cerro Toro Formation, exposed in southern Chile and deposited at high paleo latitude, display low sinuosity and an asymmetric stratigraphic structure due to the Coriolis effect.In a comment on the \citet{Peakall_2011} study, we have presented evidence that the apparent pole-ward decrease in submarine channel sinuosity is unrelated to the Coriolis force \citep{Sylvester_2013}. In the present article we expand on these ideas and present additional analysis (1) of an improved and more consistent channel sinuosity measurement and (2) of the magnitude of different forces as a function of channel size and flow behavior. In addition, we briefly discuss the impact of the Coriolis effect on overbank deposits, which is an important latitudinal effect in these systems.

ABSTRACT I show how to express functions with a known series expansion in terms of Laguerre polynomials. MAIN We have the integral representation of the Laguerre polynomials, L_n(z)= {n!}\int_0^\infty e^{-t}t^n J_0(2)\;dt, where J₀(x) is a modified Bessel function, as given on the Wolfram Functions website. If we have a function f(x) that admits a series representation f(x)=^\infty a_k x^k, with some coefficients ak, then we can define a transform on L[f] F(s)=L[f(x)]=\int_0^\infty K(x,s)f(x)\;dx. If we pick the kernel function to be K(x,s)= e^{-x}J_0(2), then we have F(s) = ^\infty a_k\int_0^\infty e^{-x}J_0(2)x^k \; dx = ^\infty {e^s}L_k(s), which is an expansion of the transformed function F(s) in terms of Laguerre polynomials. As an example, if f(x)=1, then ak = [k = 0], this gives \int_0^\infty e^{-x}J_0(2)\;dx = ^\infty {e^s}L_k(s) = {e^s} = e^{-s} this leads to an infinitely recursive integral e^{-s} = \int_0^\infty \int_0^\infty \int_0^\infty \cdots \int_0^\infty e^{-x_n}J_0(2})\;dx_n \cdots J_0(2)\;dx_3J_0(2)\;dx_2J_0(2)\;dx_1 this should also lead to the set of results e^{-s} = \int_0^\infty e^{x_1}J_0(2)\;dx_1 e^{-s} = \int_0^\infty\int_0^\infty e^{x_2}J_0(2)J_0(2)\;dx_1dx_2 e^{-s} = \int_0^\infty\int_0^\infty\int_0^\infty e^{x_3}J_0(2)J_0(2)J_0(2)\;dx_1dx_2dx_3 and so on. If we formally define a function f(x) = ^\infty {e k!k!} = {e} I_0(2) we end up with a series expansion for F(s), starting F(s) = 1 - 2s + {4}s^2 - {18}s^3 + {576}s^4 - {7200}s^5 + \cdots It seems the inverse kernel is given by K^{-1}(x,s) = ^\infty ^i {(i-j)!j!j!} = ^\infty {i!}L_i(s) such that f(x) = \int_0^\infty K^{-1}(x,s)F(s)\;ds

কাকে বলে রোগী কেন্দ্রিক চিকিৎসা? একটি চিকিৎসার কাহিনিএকটি অভিজ্ঞতার গল্প শুনুন। মাস দুয়েক আগের কথা। বাড়িতে শীর্ষাসন করতে গিয়ে মনে হয় ঘাড়ে আঘাত পেয়েছিলাম। প্রথম দু-একদিন ঘাড়ে অল্প ব্যথা করছিল । তারপর একদিন মাঝরাতে পিঠের যন্ত্রণায় ঘুম ভেঙে গেল। পিঠের ডান দিকে যন্ত্রণা হচ্ছিল, ডানহাতের বুড়ো আঙুলে সাড় ছিল না, হাত দুর্বল; তখন মনে হল কাঁধে গরম জলের ব্যাগ দিয়ে রাখি, তাহলে হয়ত আরাম হবে। জল ফুটিয়ে ব্যাগে যেই পুরতে গেছি, ফুটন্ত জল চলকে আমার ডান হাতে পড়ল, অমনি হাতের চামড়া ঝলসে গেল । একে সপ্তাহের শেষ, তায় অত রাতে ডাক্তার পাওয়া যাবে না, হাসপাতাল আমার বাড়ি থেকে বড় শহরে একশ কিলোমিটার দূরে, অতএব নিজের  প্রাথমিক চিকিৎসা  নিজেকেই করতে হল। কোন রকমে দুদিন গেল।  ততদিনে দেখা গেল যে হাতে বেশ বড়সড় একটা ফোসকা পড়েছে। ঝলসানো চামড়ার ও ফোসকার ড্রেসিং করাতে আমার পরিচিত একটি  ক্লিনিকে গেলাম। সেখানে  এক অপরিচিতা নার্স আমার চিকিৎসা করলেন। তিনি ড্রেসিং করার সময় থমথমে মুখে কাগজ দেখে মন দিয়ে কাজ করে গেলেন, আমার সঙ্গে একটি কথাও বললেন না। আমার কেমন যেন অস্বস্তি হচ্ছিল যে তাঁর সামনে একজন মানুষ বসে আছে, সে মাঝে মাঝে যন্ত্রণায় আর্তনাদ করে উঠছে, তাকে আমল দেওয়া দূরের কথা, যন্ত্রণা হচ্ছে কি না, একবার জিজ্ঞেসও করলেন না, খস খস করে কাঁচি দিয়ে, এমন ভাবে পোড়া চামড়া কেটে দগদগে কাটা ঘায়ের ওপর মলম আর পটি দিয়ে ড্রেসিং করলেন হাতটা যেন শরীরের বাইরের কোন একটা অংশ, তারপর নিপুণ হাতে পরিপাটি করে ব্যাণ্ডেজ বেঁধে দিলেন। দিয়ে  আমাকে মৃদু শাসনের সুরে বললেন, এই ভাল করে ড্রেসিং করে দিলাম, বাইরে বসে একটু জিরিয়ে নিয়ে বাড়ি চলে যান। দেখবেন যেন একটুও জল লাগাবেন না, সাত দিনে সেরে যাবে।চিকিৎসা শুরু হবার দশ দিনের মাথায় হাতের ঘা সেরে গেল, পটি খোলা হল। আমি সুস্থ হলাম। আমার চিকিৎসা যে চিকিৎসক, ফিজিওথেরাপিস্টরা,  নার্স-রা করেছেন তাঁরা সকলে অভিজ্ঞ ও দক্ষ, তাঁদের পেশাগত নৈপুণ্য প্রশ্নাতীত, ক্লিনিকটি  পরিষ্কার পরিচ্ছন্ন, তাতে প্রায় যত রকমের আধুনিক ব্যবস্থা থাকা প্রত্যাশিত সব ছিল। আমার দেশ, নিউজিল্যাণ্ডে, সরকার দেশের মানুষের চিকিৎসার ব্যয়ভার বহন করেন, তাই আমার চিকিৎসার মোট খরচ নামমাত্র, এবং আমি যথাসময়ে কোন রকম গোলমাল ছাড়াই পুরোপুরি ভাল হয়েও গেছি ।তথাপি সেদিনের নার্স ভদ্রমহিলার কাছে পাওয়া সেই নৈর্বক্তিক নিদান বলুন কি দাওয়াই, আমার মনে দাগ কেটে গেল । ব্যাণ্ডেজ করা হাতের ভেতরের যন্ত্রণা সহ্য যেমন করেছি, তেমনি আমি নিজেকে প্রশ্ন করেছি, এই যে চিকিৎসা পেলাম, এ চিকিৎসা প্রকৃত গুণমান কিভাবে বিবেচনা করব? এ চিকিৎসার গুণমান যদি নিরূপণ করতে হয়, রোগী হিসেবে তাতে চিকিৎসা পেতে গিয়ে আমার মনে যে অসন্তোষ দেখা দিল তাকে কি উপেক্ষা করব? কেন? চিকিৎসার মান শুধু কি শারীরিক ভাবে সুস্থ হয়ে যাওয়া দিয়ে বিচার করা হবে? বিশ্ব স্বাস্থ্য সংস্থার সংজ্ঞা অনুযায়ী স্বাস্থ্য কেবল শরীরের রোগমুক্তি নয়, মন ভাল হওয়া, সামাজিক ভাবে সুস্থ থাকা, সবকিছু নিয়ে \cite{3075921}। তাই যদি হবে, তাহলে রোগীর প্রতি চিকিৎসকের নৈর্বক্তিক আচার আচরণকে, যে আচরণে রোগী বিমর্ষ বোধ করেন, চিকিৎসার মান নির্ধারণে তাকেও বিচার করে দেখতে  হবে নিশ্চয়ই? কোন উপায়ে গোটা বিষয়টিকে মাপা যেতে পারে? চিকিৎসা করতে গিয়ে রোগীর পরিপ্রেক্ষিত বিচার না করা হলে সে চিকিৎসা কি মানবিক? গুণ নিরূপণ করতে গেলে সে চিকিৎসা ভাল না মন্দ? ভাল চিকিৎসার "ভাল" ব্যাপারটি কাকে বলে? অন্যদিকে  কিভাবে ভাল চিকিৎসা-প্রতিষ্ঠান চিনব? কিভাবে ভাল স্বাস্থ্য ব্যবস্থাকে চিহ্নিত করব? কিভাবে চিকিৎসার মান নিরূপণ শুধু নয়, মাপযোক করব? এই বিষয়টি নিয়ে আলোচনাই এই লেখার উদ্দেশ্য।চিকিৎসা ব্যবস্থার ও চিকিৎসার গুণমান কেন বিচার করব?আমাদের সকলের -- রোগী, চিকিৎসক, নার্স, অন্যান্য স্বাস্থ্য পরিষেবা যাঁরা দিই, এমনকি সরকারের পরিপ্রেক্ষিতেও, চিকিৎসা-ব্যবস্থার গুণমান বিচার খুঁটিয়ে দেখার একটা প্রয়োজন আছে। আমরা সবসময় চিকিৎসা ব্যবস্থা থাকা সত্ত্বেও তার সহজে নাগাল  পাই না। প্রায়ই চিকিৎসা এত সময় ও অর্থ সাপেক্ষ হয়ে পড়ে, আমরা চিকিৎসা করাতে পারি না। আবার যখন পারি, তখন নিখুঁত কারিগরের হাতে সংবেদনহীন, নৈর্বক্তিক, ও আন্তরিকতাহীন চিকিৎসা আমাদের অনেককেই সহ্য করতে হয়। আমরা যারা রোগী, তারা প্রচুর সময় ও অর্থ ব্যয় করি; তা সত্ত্বেও যে চিকিৎসা  পরিষেবা আমরা পাই তাতে আমাদের কথা কতটুকু বিচার বিবেচনা করা হয়?চিকিৎসা পরিষেবার কথা বললে তিনটি স্তরে "চিকিৎসার" কথা বলা হয়। আমারদের দেশের পরিকাঠামোয় চিকিৎসা পরিষেবা তিনটি পৃথক স্তরে দেওয়া হয় -- প্রাথমিক, মাধ্যমিক, এবং বিশেষজ্ঞ-কেন্দ্রিক চিকিৎসা ব্যবস্থা। প্রাথমিক স্তরে মূলত প্রতিষেধ-মূলক চিকিৎসা বা পরিবার কেন্দ্রিক চিকিৎসার ব্যবস্থা করা হয় । আমাদের দেশে যাঁরা সাধারণ ডাক্তারবাবু, পারিবারিক ডাক্তার, পাড়ার ডাক্তার, "ডাক্তার কাকু/জেঠু", যাঁরা বরাবর আমাদের পরিবারের কাছাকাছি থেকে চিকিৎসা করেছেন, জ্বর জারি হলে প্রথমে তাঁদের কাছে যাওয়া হয়, টিকা দিতে হলে তাঁদের শরণাপন্ন হতে হয়, এ হল সেই স্তর। এঁদের পরে মাধ্যমিক স্তরে যে ধরণের পরিষেবা দেওয়া হয় তাতে অপেক্ষাকৃত জটিল অসুখের দ্রুত নির্ধারণ ও চিকিৎসা করার ব্যবস্থা করতে হবে। তা পারিবারিক চিকিৎসকরাও করতে পারেন, বা "সাধারণ" (এখানে সাধারণ বলতে বিশেষ রোগের হাসপাতাল নয় এরকম হাসপাতাল) হাসপাতালে গিয়ে চিকিৎসা করা যেতে পারে। এর মধ্যে ওষুধের মাধ্যমে চিকিৎসা, শল্য চিকিৎসা, স্ত্রীরোগ, ধাত্রীবিদ্যা সংক্রান্ত চিকিৎসা, শিশুদের চিকিৎসা পড়ে। সরকারী হাসপাতাল, বেসরকারী নার্সিং হোম, হাসপাতাল এই ধরণের জায়গায় মানুষ চিকিৎসা করাতে যান। এর পরবর্তী  স্তরে খুব জটিল রোগের বিশেষজ্ঞ স্তরের চিকিৎসা। প্রাথমিক বা মাধ্যমিক স্তরে রোগ সারানো না গেলে মানুষকে নানা ভাবে রোগমুক্তি বা বিশেষ ক্ষেত্রে অঙ্গ- প্রতিস্থাপনার বন্দোবস্ত করা, জটিল অস্ত্রোপচার, এই ধরণের চিকিৎসা এর লক্ষ্য। এই ধরণের চিকিৎসা প্রযুক্তিগত দিক থেকে জটিল ও ব্যয়সাপেক্ষ, এর চিকিৎসা বিশেষজ্ঞরা করবেন। যে হাসপাতালে সেই চিকিৎসা হবে, তাকে স্পেশালিটি বা সুপার-স্পেশালিটি হাসপাতাল বলা হয়। ভারতে সরকারী স্বাস্থ্য দপ্তরের মানুষের কাছে স্বাস্থ্য পরিষেবার পৌঁছনর দায়িত্ব থাকে, সরকার ও সমাজ এইরকম একটি পরিকাঠামোয় পরিষেবা দেবার ব্যবস্থা করেন । এখন প্রশ্ন, চিকিৎসা পরিষেবার মান নির্ধারণ করার সময় এই তিনটি স্তরকে কিভাবে বিবেচনা করব বা তাকে কিভাবে মাপব? গুণমান নির্ধারণ করার কিবা প্রয়োজন? দ্বিতীয় প্রশ্নটিতে আসা যাক।এক, মান নির্ধারণ না বিচার করতে শিখলে, আপনি যে-ই হোন, আপনি ঠকে যেতে পারেন, এমনকি আপনার প্রাণসংশয় অবধি হতে পারে। কোন চিকিৎসা-ব্যবস্থার মান ভাল, কোনটির মান আরো ভালো, এ বিষয়টি জটিল। আমরা রুগীরা বা তাঁদের বাড়ির লোকেরা কোন বিশেষ একটি স্বাস্থ্য-সংস্থা, বা কোন একটি রাজ্যের চিকিৎসা-ব্যবস্থা, কি কোন হাসপাতালকে হয়ত ওপর থেকে দেখে ভাবছি খুব ভাল, আসলে রোগী নিয়ে সেখানে ভর্তি হতে বা চিকিৎসা পেতে গিয়ে হয়রানির শিকার হতে হয়, ভুল চিকিৎসা হতে পারে, নষ্ট সময় ও অর্থদণ্ডের কথা না হয় ছেড়েই দিলাম । আবার অন্যদিকে কোন একটি চিকিৎসা প্রতিষ্ঠানটিকে মনে মনে খারাপ ভাবছি, হয়ত সেখানে কম পয়সায় চিকিৎসা হয়, সে হয়ত বাইরে থেকে দেখতে মামুলি, তাই তাকে প্রত্যাখ্যান করলাম, অথচ সেখানেই চিকিৎসা করাতে গেলে দেখতাম তারা অতি আন্তরিক ও খুব ভাল চিকিৎসা করে। আর কিছু না হোক, অনাবশ্যক অর্থদণ্ডের হাত থেকে রেহাই পেতাম। দুই, চিকিৎসকদের কথা ভেবে দেখুন। আজকাল ভারতে হাসপাতালের ডাক্তারদের, বা প্রাইভেট প্র্যাকটিস করেন, এমন ডাক্তারদের, রোগীর বাড়ির লোকেরা বা আপামর জনসাধারণ গায়ে হাত তুলছে,  এ ধরণের অন্যায়, দুঃখজনক সংবাদ ইদানীং শোনা যাচ্ছে \cite{Ambesh2016749}। সংবাদপত্রের খবরে বহু ক্ষেত্রে দেখা যায় ডাক্তারবাবু যে চিকিৎসা করেছেন তাতে কোন ভুল নেই, তবুও তাঁকে অত্যাচার সহ্য করতে হচ্ছে । ডাক্তারবাবু ভাবছেন তিনি তাঁর জ্ঞানবুদ্ধিঅভিজ্ঞতা-প্রসূত, সাধ্যমত চিকিৎসা করেছেন, অভিজ্ঞতা ও প্রমাণের ভিত্তিতে যা চিকিৎসা তিনি করেছেন, উন্নত মানের চিকিৎসা বিচার করতে গেলে এইটুকুই যথেষ্ট। ডাক্তারের পক্ষে চিকিৎসা কতটা খরচসাপেক্ষ বা রোগী-চিকিৎসাকারী দলের পারস্পরিক সম্পর্ক বা রোগীদের রোগ নিয়ে অবহিত করা, তাদের সহজ ভাষায় বুঝিয়ে বলার ব্যাপারটি তাঁর চিকিৎসক সত্তা দিয়ে বিচার করলে গৌণ বলে মনে হবে। চিকিৎসার জটিল দিক, কারিগরি দিকটি তিনি ভাল বোঝেন, সেটিই তাঁর লক্ষ্য । অথচ চিকিৎসা ত্রুটিহীন হওয়া সত্ত্বেও তাঁকে রোগীপক্ষের অসন্তোষের শিকার হতে হল, এমনও হতে পারে তিনি হয়ত রোগীর সঙ্গে  যথেষ্ট ভদ্র ও সঙ্গত আচরণ করলেন, কিন্তু চিকিৎসাকারী দলের অন্যান্য সদস্য বা অন্যান্যরা রোগীর পরিবার বা রোগীর সঙ্গে অশিষ্ট আচরণ করাতে রোগীর বাড়ির লোক অসন্তুষ্ট হলেন, সব মিলিয়ে চিকিৎসার যাবতীয় দায়, রোগী ও তাঁর বাড়ির লোকের রোষ, বেচারা ডাক্তারবাবুর ঘাড়ে পড়ল, যেহেতু চিকিৎসা পরিষেবার তিনিই মুখ \cite{Madhiwalla_2006} । ডাক্তারবাবু চিকিৎসার মান একরকম করে ভেবেছেন, রোগী আর তাঁর বাড়ির লোকেদের চোখে সেই চিকিৎসার গুণমান আরেক রকম হয়ে দাঁড়িয়েছে। অতএব ডাক্তার ও রোগীর পক্ষ থেকে চিকিৎসার গুণের মাণ নির্ধারণের, বিশেষ করে মাপজোক করার তাগিদ আছে যাতে করে অন্তত এইটুকু বোঝা যায় যে, চিকিৎসার সামগ্রিক মানের দিক থেকে বিচার করলে কোনটি যথেষ্ট উচ্চমানের ও কোনটি নিম্নমানের তার একটা সাধারণের গ্রহণযোগ্য ব্যবস্থা থাকা উচিৎ, সে চিকিৎসার ফলাফল যাই হোক না কেন। এখানে তিনটি বিষয় বিবেচনা করার আছে। এক, ডাক্তারবাবুর দিক থেকে চিকিৎসার গুণমান শুধু রোগমুক্তি বা যথাযথ চিকিৎসা দিয়ে বিচার বিবেচনা করলে যথেষ্ট হবে না, আরো কিছু বিষয় ভেবে দেখতে হবে। দুই, চিকিৎসা কি স্বাস্থ্যের মান নিরূপণের ক্ষেত্রে আমরা প্রায়ই সরকারী, বেসরকারী, আন্তর্জাতিক, নানারকম পরিসংখ্যানের সাহায্য নিই। পাঁচ বছর বয়সের কম বয়সী শিশু মৃত্যু, বা চিকিৎসক-পিছু কত শয্যা, সেই সংখ্যার নিরিখে গোটা স্বাস্থ্যব্যবস্থার সামগ্রিক মান নিরূপণের একটা আবছা ছবি আমরা পাই। চিকিৎসা/স্বাস্থ্য ব্যবস্থার মান নির্ধারণ করতে গিয়ে তাতে কিছুটা আন্দাজ পাওয়া যেতে পারে হয়ত, তবে সে নেহাতই মোটা দাগের মাপ। এই ধরণের পরিমাপ যেহেতু সামগ্রিক তথ্য পরিসংখ্যান দিয়ে করা হয়, তাতে ব্যক্তিবিশেষের ক্ষেত্রে কি প্রযোজ্য তা বোঝা যাবে না । তিন, রোগীর পরিপ্রেক্ষিত বাদ দিয়ে রোগ নিদানের গুণমান বিচার করা এক্ষেত্রে  অর্থহীন। রোগমুক্তির বিচার যাঁরা রোগের পরিষেবা দেন, বা রোগীর পরিপ্রেক্ষিত বাদ দিয়ে করবেন কি করে? আর করবেনই বা কেন? গুণমানের মাপযোকের ব্যাপারটি আলোচনার করার আগে আরো দুটো কথা বলার আছে -- এক, স্বাস্থ্য বা চিকিৎসা ব্যবস্থার শরিকদের চিনে নিতে হবে, আর দুই, পরিকাঠামো বলতে কি বোঝাতে চাইছি সেটি স্পষ্ট হওয়া চাই।

The social and organizational history of humanity is intricately entangled with the history of technology in general and the technology of information in particular. Advances in this area have often been closely involved in social and political transformations. While the contemporary period is often referred to by such names as the Computing and Information Age, this is the culmination of a series of historical transformations that have been centuries in the making. This course will provide a venue for students to learn about history through the evolution of number systems and arithmetic, calculating and computing machines, and advanced communication technology via the Internet. Students who take this course will attain a degree of technological literacy while studying core historical concepts. Students who complete this course will learn the key vocabulary of the computing discipline, which is playing a significant role in modern human thought and new media communications. The History of Computing will be organized around the historical perspective. The relationships between social organization, intellectual climate, and technology will be examined and stressed.

Dynamical gauge fields are a fundamental concept of high-energy physics. However, learning about them typically takes enormous amounts of time and effort. As such, they are typically a bit mystical to students (including me) of other fields of physics like condensed-matter or AMO. Here, we will give a simple introduction into some of the concepts that might allow for the quantum simulation of these theories with ultracold atomic gases.The reader should know about second quantization and the basics of quantum mechanics as the arguments are based on this formalism.

IntroductionA colleague recently proposed submitting an article about work to which my lab had contributed to the journal Neurology. I said, Neurology is a fine journal—some of my favorite authors have published there (smile)—but, like many traditional journals, they don't allow authors to re-use their own words for future book chapters. That's true even if a pre-publication version ends up later on PubMed Central. At least, they don't allow this without their deciding whether to deign to grant permission in each case. It may surprise you to know that many traditional / "hybrid" journals that tout an Open Access option—usually an expensive one—allow only a noncommercial license (like the CC BY-NC license). That sounds fine until you learn that adapting your own words to contribute to a book or to a site like eMedicine counts as commercial use! Personally, in an age in which the "Paper User Interface" is almost obsolete, and I almost always find papers from PubMed or Google, giving my rights away to a journal (by copyright transfer or an exclusive license to publish) is just ridiculous.I replied to my colleague suggesting she submit instead to a journal that allowed the authors to re-use their own words freely (as with the CC BY license), and went on to explain other benefits of fully open access publishing. I've discussed some of these advantages elsewhere \cite{25580234}. She replied, "I'm curious to know how publishing in these open access platforms has been received by your department? There's a clear message in mine that they want to see pubs in journals with good impact factors, especially for promotion consideration." This is a reasonable concern, of course, and a common one, and I acknowledged that at my career stage the pressure is not on me to the same extent. But I gave her some thoughts anyway, and then I realized that others might find them interesting. So here they are.The real answerThe real answer is for leaders to judge papers (much less faculty) on different metrics. The JIF was never meant to grade the quality of an individual paper, and it does it poorly. Even collectively, higher impact factor journals are more likely to publish articles that are retracted than are lower impact factor journals (among other reasons, think about this: “novel” results imply a lower prior probability of truth). Besides, if by impact you mean total number of citations, some OA journals are way in front (e.g. Frontiers in Psychology is the most cited multidisciplinary psychology journal in the world, and there have been something over 200,000 citations to articles in PLOS ONE).Being down on the journal impact factor (JIF) is not just my opinion. You can listen to some Nobel laureates criticizing it here.Some young scientists are adopting an open-only policy and let the chips fall where they may, and several of these scientists have been quite successful. In the meantime . . .But in the meantime, here are some options for those in my colleague's position. First, there are open access  journals with a high JIF. Here is a short list of a few open access journals I've published in or considered, to show the wide range of JIFs for journals that allow authors to keep their rights:

The current crisis of veracity in biomedical research is enabled by the lack of publicly accessible information on whether the reported scientific claims are valid. One approach to solve this problem is to replicate previous studies by specialized reproducibility centers. However, this approach is costly or unaffordable and raises a number of yet to be resolved concerns that question its effectiveness and validity. We propose to use an approach that yields a simple numerical measure of veracity, the R-factor, by summarizing the outcomes of already published studies that have attempted to test a claim. The R-factor of an investigator, a journal, or an institution would be the average of the R-factors of the claims they reported. We illustrate this approach using three studies recently tested by a replication initiative, compare the results, and discuss how using the R-factor can help improve the veracity of scientific research.

Tam Hunt, UC Santa Barbara, tam.hunt@psych.ucsb.eduThe Lorentz transformations form the mathematical core of the 1905 theory of Special Relativity as well as the earlier version of relativity created by Lorentz himself, originally in 1895 but developed further in the ensuing years. These two theories interpret the physical significance of the transformations quite differently, but in ways that are generally not considered to be empirically distinguishable. It is widely believed today that Einstein’s Special Relativity presents the superior interpretation. A number of lines of evidence, however, from cosmology, quantum theory and nuclear physics present substantial evidence against the Special Relativity interpretation of the Lorentz transformations, challenging this traditional view. I review this evidence and suggest that we are now at a point where the sum of the evidence weighs against the Special Relativity interpretation of the transformations and in favor of a Lorentzian or neo-Lorentzian approach instead.1. IntroductionI’m sitting in a public square in Athens, Greece, biding my time as I write these words. The battery on my phone ran out as I was trying to navigate to my lodgings on my first night in this historic city, forcing me to stop and charge my phone for a little while. I’m waiting for the passage of time.The nature of time has been debated vigorously since at least the age of Heraclitus and Parmenides in ancient Greece. “All things flow,” said Heraclitus. “Nothing flows,” said Parmenides as a counter-intuitive rejoinder, suggesting that all appearances of change are an illusion. How could Parmenides make the case that nothing flows, nothing changes? It would seem, from easy inspection of the world around us that indeed all things do flow, all things are always changing. So what was Parmenides talking about?Parmenides’ arguments illustrate well the rationalist approach that Plato was later to more famously advocate, against the empiricist or “sensationist” approach that Heraclitus and Aristotle too would champion as a contrary approach. Parmenides and Plato saw reason as the path toward truth and they were not afraid to allow reason to contradict what seemed to be obvious sensory-based features of the world. Apparent empirical/sensory facts can deceive and, for these men, Parmenides, Plato and their followers, reason alone was the arbiter of truth. Wisdom entailed using reason to see through the world’s illusions to the deeper reality.Heraclitus and Aristotle, to the contrary, stressed the need to be empirical in our science and philosophy (science and philosophy were the same endeavor in the era of classical Greece). Reason was of course a major tool in the philosopher’s toolbox for these men too, but it seems that reason unmoored from evidence should not be used to trump the obvious facts of the world. The Aristotelian approach is to find a pragmatic balance between empirical facts and reason in attempting to discern the true contours of reality.Einstein was firmly in the camp of Parmenides and Plato (Popper, et al. 1998). He famously considered the passage of time, the distinction between past, present and future, to be a “stubbornly persistent illusion.” This view of time, as an illusory construct hiding a deeper timeless world, was based on his theories of relativity. Einstein and his co-thinkers held this view, of time as illusory, despite the obvious passage of time in the world around us, no matter where we look. The widely-held view today is that Einstein finally won the long war, decisively, between Heraclitus and Parmenides. Despite appearances, nothing flows and the passage of time is just that: only appearance.I suggest in this paper, however, that this conclusion is premature. Einstein’s thinking is indeed an example of rationalism trumping empiricism and it is time for us to take a more empirical approach to these foundational questions of physics and philosophy. Today’s physics lauds empiricism rhetorically, but in practice a rationalist approach often holds sway, particularly with respect to the nature of time.2. An overview of Special Relativity and Lorentzian RelativityIn discussing the nature of time with respect to modern physics, I will focus on the Special Theory of Relativity (SR) and avoid discussion of the general theory. Einstein’s 1905 theory of relativity adopted the Lorentz transformations directly, unchanged from Lorentz’s own version of these equations (Einstein 1905, Lorentz 1895 and 1904, in Lorentz 1937). Einstein’s key difference from Lorentz’s version of relativity (first put forth in 1895, but developed further in later work) was to reinterpret Lorentz’s equations, based on a radically different assumption about the nature of physical reality. Lorentz interpreted the relativistic effects of length contraction and time dilation—which follow straightforwardly from the Lorentz transformations—as resulting from interaction with an ether that constituted simply the properties of space (Lorentz’s ether was not some additional substance that pervades space, as was the case in some earlier ideas of the ether). Einstein, to the contrary, interpreted these effects as resulting from the dynamics of spacetime, a union of space and time into a single notion, and dismissed the ether as “superfluous.”Because Lorentz’s and Einstein’s versions of relativity both use the Lorentz transformations, they will yield in many cases the same empirical predictions. The prevailing view today, then, is that while these two theories are empirically indistinguishable there are other considerations, relating to parsimony primarily, that render special relativity the preferred approach. I discuss below, however, why we now have good empirical reasons to distinguish between these two interpretations—in favor of the Lorentzian approach.Length contraction and time dilation occur as a result of the assumed absolute speed of light because either space or time, or both, must distort if we consider the speed of light to be invariant. This is because speed is measured simply by dividing distance traveled by the time elapsed; and if the speed of light remains the same in all circumstances then space and/or time must distort in order to maintain this invariance. As an object travels closer and closer to the speed of light, its length must decrease (length contraction) and/or the time elapsed must increase (time dilation) – but only from the perspective of an observer in a different inertial frame. In the original inertial frame there is no length contraction or time dilation.“Moving clocks run slow” is a good shorthand for relativistic time dilation, but again only from the perspective of a different inertial frame. Time moves at the same rate for an observer in the moving frame of reference, no matter what one’s speed in relation to other frames. Relativistic effects only occur when considering the relationship between two different frames of reference, not in the same frame.

ABSTRACT This work strongly relates to Lambert series, but uses an alternative kernel in the transformation. Many results are shown from experimental techniques and tabulated below. MAIN From the product representation of ez we can write x = ^\infty {k} \log(1-x^k) or perhaps more nicely x = ^\infty {k} \log\left({1-x^k}\right) I then wonder what other functions can be written in terms of this, for example e^x -1 = ^\infty {k!}\log(1-x^k) where the ak starting from a₁ are −1, 0, 1, 5, 23, 59, 719, 839 which appear to be A253901 minus 1, an then we have e^x \approx 1+^\infty {k!}\left((d-1)!^{\mu\left({d}\right)}-1\right)\log(1-x^k) but this seems to be wrong for the 12th power and some others, so this is not the full story! We seem to have x^2 = ^\infty {k} \log(1-x^{2k}) in fact it seems x^n = ^\infty {k} \log(1-x^{nk}) which is fairly obvious from taking the power of the argument, however we could also have squared the entire sum, so we know that ^\infty {k} \log(1-x^{2k}) = \left(^\infty {k} \log(1-x^{k})\right)^2 and more generally ^\infty {k} \log(1-x^{nk}) = \left(^\infty {k} \log(1-x^{k})\right)^n interestingly we can write \log(1-x^m)= ^\infty ^\infty {nk}\log(1-x^{mnk}) and we must have the expansion e^x =1 -^\infty ^\infty {n!k}\log(1-x^{nk}) we can get from this the generating function of the Bell Numbers e^{e^x-1}= ^\infty ^\infty (1-x^{nk})^{{kn!}} of course this is all for x < 1. The product seems to converge for constants for example ee1/2 − 1. Other interesting results {(1-x)} = ^\infty ^\infty {k}\log(1-x^{nk}) {(1-x)^2} = ^\infty ^\infty -n{k}\log(1-x^{nk}) O\left[{\zeta(s-1)}\right] = ^\infty ^\infty {k}\log\left({1-x^{nk}}\right) ^\infty A101035(n){n} = ^\infty ^\infty \mu(n)\mu(k)\log\left({1-x^{nk}}\right) -\log(1-x) = ^\infty ^\infty \mu(n)\log\left({1-x^{nk}}\right)\\ -\log(1-x) = ^\infty ^\infty \mu(k)\log\left({1-x^{nk}}\right)\\ -\log(1-x) = ^\infty ^\infty {nk}\log\left({1-x^{nk}}\right)\\ -\log(1-x) = ^\infty ^\infty {nk}\log\left({1-x^{nk}}\right)\\ ^\infty d\tau(d)x^n = ^\infty ^\infty \log\left({1-x^{nk}}\right)\\ where O hypothetically maps a Dirichlet generating function to an ordinary generating function. The last one is a statement that ^\infty e^{ d \tau(d) x^n}= ^\infty ^\infty {1-x^{n k}} this has a few similarities to the Euler product of the zeta function \zeta(s) = } {1-p^{-s}} if we let x = 1/p, then we get ^\infty e^{ d \tau(d) p^{-n}}= ^\infty ^\infty {1-p^{-n k}} ^\infty e^{d \tau(d) p^{-n}}= ^\infty ^\infty {1-p^{-n k}} this then is a relation ^\infty e^{d \tau(d) p^{-n}}= ^\infty {({p^n};{p^n})_\infty} interestingly we could write ^\infty e^{d \tau(d) p^{-n}}= \left(^\infty {1-p^{-k}}\right)^\infty ^\infty {1-p^{-n k}} then take the product over all primes }^\infty e^{d \tau(d) p^{-n}}}{^\infty ^\infty {1-p^{-n k}}}= }\left(^\infty {1-p^{-k}}\right) }^\infty e^{d \tau(d) p^{-n}}}{^\infty ^\infty {1-p^{-n k}}}= ^\infty\zeta(k) of course this is probably nonsense OTHER INTERESTING SUMS we can change μ(n) to be something else for example we seem to have ^\infty^\infty {k}\log\left({1-x^{kn}}\right) = ^\infty d(n)x^n ^\infty^\infty {nk}\log\left({1-x^{kn}}\right) = ^\infty {n}x^n ^\infty^\infty {1}\log\left({1-x^{kn}}\right) = ^\infty {n}x^n for Euler totient function φ(n) and divisors d(n). ^\infty^\infty k\log\left({1-x^{kn}}\right) = ^\infty {n}x^n ^\infty^\infty \sigma_0(k)\log\left({1-x^{kn}}\right) = ^\infty {d})\tau(d)}{n}x^n ^\infty^\infty k^2\log\left({1-x^{kn}}\right) = ^\infty {d})}{n}x^n ^\infty^\infty {k}\log\left({1-x^{kn}}\right) = ^\infty {n}x^n other results are,k/n transforms to A007433,(k − 1)/k transforms to A069914/n. We seem to have ^\infty^\infty {n}\left(\mu(d)\mu\left({d}\right)\right)\log\left({1-x^{kn}}\right) = ^\infty {n}x^n ^\infty^\infty \left(\mu(d)\mu\left({d}\right)\right)\log\left({1-x^{kn}}\right) = ^\infty {n}\left(d \mu(d)\right)x^n ^\infty^\infty \lambda(n)\log\left({1-x^{kn}}\right) = ^\infty (n)}{n}x^n OTHER ^\infty^\infty \lambda_3(n)\log\left({1-x^{kn}}\right) = -\log(1-x)+^\infty x^{n^3} + ^\infty ^\infty }{n} where λ₃(n) is the equivalent of the Liouville function for squares but for cubes.

We demonstrate that, under Lorentz transformation, the frequency and the energy of an electromagnetic wave train form a linear relationship, emulating the equation of photon energy E = ℏω. This shows that wave-particle duality of light is compatible under space time transformation.

ABSTRACT This document notes down expressions for a few common functions in terms of Hermite polynomials. There are clear symmetries between certain special functions, i.e. cos and sin, but interestingly a similar symmetry is formed between the Gaussian and the product of a Gaussian and the imaginary error function. The method of finding these expansions comes primarily from the Hermite transform. An approximate form for the log function is given, but this may have complex branching problems. MAIN Hermite Series Couplings: We can write a few common functions in a basis of Hermite polynomials e^{ax} = ^\infty }{2^n n!}H_n(x)\\ e^{x-{4}} = ^\infty {2^n n!}\\ e^{-x^2} = ^\infty {2^{2n}(2n)!}H_{2n}(x) \\ e^{-x^2} = \left[^\infty {2^{n}(n)!}H_{n}(x) \right] \\ ?(x) = \left[^\infty {2^{n}(n)!}H_{n}(x) \right] \\ \cos(ax) = \left[^\infty {e^{a^2/4}2^{n}n!}H_{n}(x)\right]\\ \sin(ax) = \left[^\infty {e^{a^2/4}2^{n}n!}H_{n}(x)\right]\\ x^n = {2^n} ^{\lfloor {2} \rfloor} {m!(n-2m)! } ~H_{n-2m}(x) where Hn(x) is a Hermite polynomial of order n. I want to find standard forms such that a function can be written f(x) = ^\infty c_n H_n(x) for some constants cn. It is interesting to see that there is a function marked as ?(x) above, which is made of the imaginary parts of the expansion of e−x². I would like to know what it is. We can see that ?(0)=0\\ ?(\infty)=0 and it has a single maximum just greater than x = 1. It seems we can write the Taylor expansion of this function as ?(x) = x - }{3}x^3 + }{15} x^5 - }{21} x^7 + \cdots \\ we can see then it looks like {} = ^\infty 2^{n-1}}{(2n-1)!!} x^{2n-1} \\ ?(x) = {2}}(x)e^{-x^2} For the logarithm, by experimental techniques we can formally write something like \log(x) = {2}(i\gamma + \pi + i\log(4)) + }{2^{2n-1}(2n-1)!}H_{2n-1}(x) + 24^{n-1}(n-1)!}{2^{2n}(2n)!}H_{2n}(x) but it’s not clear how it converges, perhaps something slightly wrong with this. Other functions use hypergeometric expressions as coefficients, for example \cosh() = ^\infty {4},{4};{256})}{2^n (2n)!}H_n(x) by setting x = 0, this gives us some sums for unity ^\infty {4},{4};{256})}{2^n (2n)!}}{\Gamma({2})} = 1 for the exponential expression ex − 1/4 given above we get ^\infty }{n!\Gamma({2})} = 1 also ^\infty {(2n)!\Gamma((1-n)/2)\Gamma(n+1/2)} \,_0F_4(;1/4 + n/2, 1/4+n/2,3/4+n/2,3/4+n/2;1/64) = 1 and {\pi^{5/2}}=^\infty }{(2n)!\Gamma({2}-n)} \,_0_4\left(;n+{4},n+{4},n+{4},n+{4};1/64\right) It seems that in general we have the result D_{2n-1} e^{-x^2} = ^\infty (2n+2k)!}{(2k+1)!(n+k)!}x^{2k+1} = {n!} \;_1F_1\left(n+{2},{2},-x^2\right) NICE RELATIONSHIP/TRANSFORM Using related functions above seems to make in interesting transform kernel, however, there does not seem to be a one to one mapping between transformed functions and input functions. Some results are given below: ^ \infty {8a}}J_0(x)}{} = I_0(a) ^ \infty {8a}}I_0(x)}{} = J_0(a) ^ \infty {8a}}e^x}{} = e^{3a} ^ \infty {8a}}e^x}{} = e^a ^ \infty {8a}}\cos(x)}{} = e^{-a} ^ \infty {8a}}\cos(x)}{} = e^{-3a} ^ \infty {8a}}\sin(x)}{} = 0 ^ \infty {8a}}\sin(x)}{} = 0 ^ \infty {8a}}J_2(x)}{} = I_1(a) ^ \infty {8a}}J_4(x)}{} = I_2(a)

Time-resolved pump-probe measurements of Xe, pumped at 133 nm and probed at 266 nm, are presented. The pump pulse prepared a long-lived hyperfine wavepacket, in the Xe 5p⁵(²P1/2∘)6s ²[1/2]₁∘ manifold (E=77185 cm −1=9.57 eV). The wavepacket was monitored via single-photon ionization, and photoelectron images measured. The images provide angle- and time-resolved data which, when obtained over a large time-window (900 ps), constitute a precision quantum beat spectroscopy measurement of the hyperfine state splittings. Additionally, analysis of the full photoelectron image stack provides a quantum beat imaging modality, in which the Fourier components of the photoelectron images correlated with specific beat components can be obtained. This may also permit the extraction of isotope-resolved photoelectron images in the frequency domain, in cases where nuclear spins (hence beat components) can be uniquely assigned to specific isotopes (as herein), and also provides phase information. The information content of both raw, and inverted, image stacks is investigated, suggesting the utility of the Fourier analysis methodology in cases where images cannot be inverted.

ABSTRACT The District Attorney’s office of Santa Clara County, California has observed long durations for their prosecution processes. It is interested in assessing the drivers of prosecutorial delays and determining whether there is evidence of disparate treatment of accused individuals in pre-trial detention and criminal charging practices. A recent report from the county's civil grand jury found that only 47% of cases from 2013 were resolved in less than year, far less than the statwide average of 88%. We describe a visualization tool and analytical models to identify factors affecting delays in the prosecutorial process and any characteristics that are associated with disparate treatment of defendants. Using prosecutorial data from January through June of 2014, we find that the time to close the initial phase of prosecution (the entering of a plea), the initial plea entered, the type of court in which a defendant is tried and the main charged offense are important predictors of whether a case will extend beyond one year. Durations for prosecution are found not significantly different for different racial and ethnic population, and do not appear as important features in our modeling to predict case durations longer than one year. Further, we find that, in this data, 81% of felony cases were resolved in less than one year, far greater than the value reported by the civil grand jury.

Prior research demonstrates that improved medication adherence can produce substantial total health care savings. However, limited evidence exists to support the value of interventions to improve medication adherence. This article describes a method using alerts mailed to prescribers to improve adherence to antidepressants. The primary aim of the study evaluated the impact of written, patient-specific medication adherence alerts mailed to prescribers on overall depression-related health care costs associated with the use of antidepressant medications. The study used a clinical alert system that integrates medical and pharmacy claims data to identify and notify prescribers about patient-specific care gaps in the outpatient setting. This retrospective and observational study used health care claims from a high-risk population to match patients, identify conditions, and identify early discontinuation of antidepressant medications. The claims also allowed us to calculate changes in overall health care costs related to depression. The results show that mailing an alert to the prescriber increases the number of patients that have prescriptions for antidepressants six months after an alert from approximately 8% to 35%.  The analysis further indicated that when a patient restarts their antidepressant and continues for at least six months, their follow-up medical plus pharmacy costs will be approximate $2,671 less than if they remain non-compliant. The study supports the use of a computer system to integrate health care claims data, identify care gaps, and generate written alerts to be mailed to prescribers as a means to improve patient adherence and lower total health care costs in patients receiving antidepressants.

Clive E Adams1, Alan A Montgomery2, Tony Aburrow3, Sophie Bloomfield4, Paul Briley4, Ebun Carew4, Suravi Chatterjee-Woolman4, Ghalia Feddah4, Johannes Friedel5, Josh Gibbard4, Euan Haynes6, Mohsin Hussein4, Mahesh Jayaram7, Samuel Naylor4, Luke Perry7, Lena Schmidt5, Umer Siddique4, Ayla Tabaksert4, Doug Taylor8, Aarti Velani4, Douglas White4, Jun Xia91. Institute of Mental Health, University of Nottingham, UK2. Nottingham Clincial Trials Unit, University of Nottingham, UK3. John Wiley and Sons, Ltd.4. The Deanery, University of Nottingham, UK5. Hochschule Furtwangen University, Furtwangen im Schwarzwald, Germany6. The Deanery, University of Newcastle, UK7. University of Melbourne, Australia8. Wikipedian9. Systematic Review Solutions, UK.Contact:Professor Clive E AdamsInstitute of Mental HealthJubilee CampusUniversity of Nottingham Innovation ParkTriumph RoadNottinghamNG7 2TUPhone: 0115 823 1294Email: clive.adams@nottingham.ac.uk

ABSTRACT Differentiation under the integral sign is a common technique for solving various integrals. This article investigates briefly a few applications of applying an entire series of differential operators to an integral. If the general form of the nth derivative is known, a series representation of the integral can be given, however they appear to tend to hypergeometric functions which cannot be reduced easily. MAIN I note down some identities for differential operators. It seems that a function of the differential element Dan (diff w.r.t a, n times) applied to the exponential function just goes to the product of the two functions. For Bessel functions I₀ and J₀ we have the following J_0(D_a)e^{\pm a x} = J_0(x)e^{\pm a x}\\ J_0(D_a)e^{\pm i a x} = I_0(x)e^{\pm i a x}\\ J_0(D_a)\sin(ax) = I_0(x)\sin(ax)\\ J_0(D_a)\cos(ax) = I_0(x)\cos(ax)\\ J_0(D_a)\sinh(ax) = J_0(x)\sinh(ax)\\ J_0(D_a)\cosh(ax) = J_0(x)\cosh(ax) these results make sense as the trigonometric or hyperbolic trigonometric functions are linear combinations of either the complex of real exponential functions. Interestingly we have J_0(D_a)\log(a x) = \log(ax) + \log\left({2}\left(1+{a}}\right)\right) Now say we want to evaluate the integral I=\int_0^\pi I_0(x)\sin(a x)\; dx something Mathematica fails to do for general x. From the above identities we can write I = J_0(D_a)\int_0^\pi \sin(a x) \; dx \\ I = J_0(D_a){a}\\ I = J_0(D_a)\left[{a}\right] - J_0(D_a){a}\\ now we need to know the general derivative of these function to calculate the series. We have D^n_a {a} = {a^{n+1}}\\ D^{2n}_a {a} = {a^{2n+1}} This gives J_0(D_a)\left[{a}\right] = ^\infty {4}\right)^n}{(n!)^2}{a^{2n+1}} = {a{a^2}}} for the next term things are less easy, we have a reccurence relation for the general derivative, looking for a pattern it seems that D_a^{2n}\left[{a}\right] = {a^{2n+1}} for polynomials Pn and Qn we seem to have P_n = ^n {(2k)!} (\pi a)^{2k}\\ Q_n = 2n\pi a^{n-1} {(2k+1)!} (\pi a)^{2k} we then have D_a^{2n}\left[{a}\right] = \Gamma (2 n+1) \left((-1)^n 2^{-2 (n+1)} \pi ^{2 n+{2}} \left(\pi a \cos (\pi a) \, _1_2\left(1;n+{2},n+2;-{4} a^2 \pi ^2\right)-2 \sin (\pi a) \, _1_2\left(1;n+1,n+{2};-{4} a^2 \pi ^2\right)\right)+a^{-2 n-1}\right) which gives us J_0(D_a)\left[{a}\right] = ^\infty {4}\right)^n}{(n!)^2}\Gamma (2 n+1) \left((-1)^n 2^{-2 (n+1)} \pi ^{2 n+{2}} \left(\pi a \cos (\pi a) \, _1_2\left(1;n+{2},n+2;-{4} a^2 \pi ^2\right)-2 \sin (\pi a) \, _1_2\left(1;n+1,n+{2};-{4} a^2 \pi ^2\right)\right)+a^{-2 n-1}\right) this is not easy to solve, however for a = 2 this breaks down into two terms ^\infty {4}\right)^n}{(n!)^2} {2^{2n}} = {} this will cancel with the simple term of opposite sign which also evaluates to $1/$ for n = 2, the is also a more complicated hypergeometric term which then takes the entire value of the integral ^\infty \, _1F_2\left(1;n+{2},n+2;-\pi ^2\right)}{4^n(n+1) (2 n+1) (n!)^2} = 1.87316339431\cdots so we have \int_0^\pi I_0(x)\sin(2x)\;dx = -^\infty \, _1F_2\left(1;n+{2},n+2;-\pi ^2\right)}{4^n(n+1) (2 n+1) (n!)^2} at this stage, it’s unclear how to manipulate further. We have generated a series representation of the value of the original integral. NEXT EXAMPLE Trying another integral \int_0^\infty J_0(x^2)\exp(-a x^2)\; dx =}{2} J_0(D_a)\left[ {}\right] we have D_a^{2n} {} = {16^n (2n)! a^{2n-1/2}} as a result \int_0^\infty J_0(x^2)\exp(-a x^2)\; dx = }{2}^\infty {64^n (2n)!(n!)^2}{a^{2n-1/2}} and this time a tractable form can be reached in terms of the complete elliptic integral K \int_0^\infty J_0(x^2)\exp(-a x^2)\; dx = {2}-{2}\right)}{(1+a^2)^{1/4}} using the Mathematica convention for the complete elliptic K integral, where the argument is the modulus squared. We could potentially apply this trick again and again to get higher integer powers of the Bessel functions in the integrand.

A document by Mazen A. Afif. Click on the document to view its contents.

ABSTRACT This document gives a short list of transform pairs for an integral transform which resembles a Mellin transform on reduced support [0, 1] rather than [0, ∞]. There is a deep connection between functions here. There may be use from this transform in evaluating series expansions at ∞, especially if a large enough table of transform pairs was generated. MAIN Define an integral transform Q on a function f(x). q(s)=\int_0^1 x^{s-1} f(x) \; dx = Q[f] which mimics the Mellin transform over a smaller interval. TABLE OF RESULTS f(x) & q(s) \\ 1 & {s}\\ x^n & {n+s}\\ {n!} & {(s+m)^{n+1}}\\ {x-1} & \psi^{(n)}(s)\\ -x\log x & {(1+s)^2}\\ {\log x} & \log\left(1+{s}\right)\\ e^{a x} & (-a)^{-s}(\Gamma(s)-\Gamma(s,-a))\\ \log(a x) & {s^2}\\ _0(a x) & {s}\;_1F_2({2};1,1+{2};{4})\\ \cos(a x) & {s}\;_1F_2({2};{2},1+{2};-{4})\\ x^{a/b}&{a+b s}\\ \log(x) \log(1+x) & {4 s^2}\left(\log 16 - 2\psi_0(1+{2})+2\psi_0({2}) +s\psi_1(1+{2})-s\psi_1({2}) \right)\\ \sin(x) & {1+s}\;_1F_2({2}+{2};{2},{2}+{2};{4})\\ \;_2F_1(a,b;c;z) & {s}\\ L_n(x) & {s}\;_2F_2(-n,s;1,1+s;1)\\ -{2x} & {(s-1)^3} SOME EXAMPLES OF THE ABOVE as a result of the expansion at x = ∞ of \log\left(1+{x}\right)=^\infty }{kx^k} we have Q_{x\to s}\left[{\log x}\right] = \log\left(1+{s}\right) HYPERGEOMETRIC FLEXIBILITY Say we want to analyse the derivatives of a hypergeometric function. We can potentially do this by converting it to it’s integral form through the above table, then differentiating, and then reintegrating. HYPERGEOMETRIC INCREMENT AND DECREMENT OPERATORS We can define some operators O that increment or decrement the arguments of a hypergeometric function. For example O{0,-1}\;_1F_2(a;b,c;z)=\;_1F_2(a;b,c-1;z) then we have that O{0,-1}Q_{x \to s}[\sinh(a x)]={1+s}\\ O{0,-1}Q_{x \to s}[\cosh(a x)]={s} some information regarding the integral transform Q appears to be expressed nicely in this manner.

Early in the course of Parkinson disease (PD), treatment usually goes well. However, after five to ten years, things start to change as treatment requires higher doses of medications and side effects become more problematic. One of the most difficult problems is the development of hallucinations or delusions. Throughout the 20th century, treatment options were unproven and unsatisfactory, but the past 20 years have brought important changes. Two medications that are well tolerated in PD have now proved efficacious in randomized, controlled trials, and others are in development. Here I summarize this history briefly and provide a general plan for treating the patient with PD complicated by psychotic symptoms.

ABSTRACT This short document notes an application of Ramanujan’s Master Theorem (RMT) evaluating sums. MAIN The Master theorem states that for functions admitting an expansion of the form f(x) = ^\infty {k!} \phi(k) x^k where ϕ(k) are some coefficients, the Mellin transform of the function f(x) is given by \int_0^\infty f(x) x^{s-1} \; dx = \Gamma(s)\phi(-s) this relationship doesn’t always hold, it depends on how ϕ can be extended to negative arguments and whether the function f permits a Mellin transform ℳ[f]. For functions that do meet these criteria we can exploit this relationship not only to evaluate integrals (which was one of the original uses of the RMT), but to help evaluate sums if the inverse Mellin transform can be computed. If we take the inverse Mellin Transform of both sides of the RMT, then we have f(x) = ^{c+i \infty} x^{-s}\Gamma(s)\phi(-s)\;ds if we know the inverse Mellin transform of Γ(s)ϕ(−s), then the sum can be known. Take for example the sum containing a hypergeometric function C_1 = ^\infty {n!}\;_1F_1(-n,3,1) through This Table we can see the inverse Mellin transform of Γ(s) ₁F₁(s, 1 + ν, 1). If we let f(x) = ^\infty {n!}\;_1F_1(-n,1+\nu,1) x^n \\ f(x) = ^{c+i \infty} x^{-s}\Gamma(s)\;_1F_1(s,1+\nu,1)\;ds we can find that when x = 1, ^\infty {n!}\;_1F_1(-n,3,1) = {e} = f(1) = C_1 where I₂(x) is a modified Bessel function of the first kind. Mathematica does not appear to be able to solve this sum directly, but the result agrees numerically. HOW USEFUL IS THIS RESULT To use this result, one must know the inverse Mellin transform of some function Γ(s)ϕ(−s). In practice, it is fairly easy to compute the forward Mellin transform, and any function g(x), such that ℳ[g]=Γ(s)ϕ(−s) that can be found should work. Some examples: The trivial case is the following, we known the Mellin transform of e−x is Γ(s), so this is in effect the case ϕ(−s)=1. As a result the inverse Mellin transform of Γ(s)ϕ(−s) is e−x, then we can write ^\infty {k!}x^k = e^{-x} which we known to be true. A slightly less trivial example is that the Mellin transform of xe−x is sΓ(s), so then ϕ(−s)=s this gives the sum ^\infty {k!} (-k)x^k = x e^{-x} a more reasonable example is that [e^{-x}I_0(x)]=\Gamma({2}-s)\Gamma(s)}{\Gamma(1-s)} giving \phi(s)= \Gamma({2}+s)}{\Gamma(1+s)} and then ^\infty {k!}\Gamma({2}+k)}{\Gamma(1+k)}x^k = e^{-x}I_0(x) the lesson to take home is that if you know the Mellin transform of a function and it contains a factor of Γ(s), you can get a series representation for that function. If it doens’t contain a factor of Γ(s), there might be a problem.

I am making a list of of transforms under the integral sign, such that when a Mellin transform is applied to the original integrand with respect to an introduced parameter we get an expression for the result as the inverse Mellin transform of a bunch of gamma, zeta and cosec functions. For example \int_0^\infty{4\,x}\right)}{e^{}-1}\mathrm dx=\pi^2\left(\log}{\Gamma({4})^2}-{8}\right)+2\pi C, as is taken from Stack Exchange, but then if we introduce a parameter a \int_0^\infty{4\,x}\right)}{e^{a }-1}\mathrm dx _{} \Gamma(s)\zeta(s) \int_0^\infty x^{-s/2}\log(1+{4x}) \; dx ans then the original result can be expressed through the inverse Mellin transform as \pi^2\left(\log}{\Gamma({4})^2}-{8}\right)+2\pi C = {2\pi i}^{c + i \infty} a^{-s}\pi^{3-s}}{2-s} \Gamma(s)\zeta(s)\csc\left({2}\right) \; ds How do these integrals work? We pick a suitable c, for example {e^a-1} = {2\pi i} ^{c + i \infty} a^{-s}\Gamma(s) \zeta(s) \; ds SOME ADDITIONAL EXAMPLES Seems that \int_0^\infty \left[}{1+ax} ^\infty (1 + b_k a^k x^k)\right] \; da = \pi^\infty ( (-1)^k + b_k) x^{-s}\csc(\pi s) \int_0^\infty \left[}{1+ax} ^\infty (1 + b_k a x^k)\right] \; da = \pi^\infty ( b_k x^{k-1} -1) x^{-s}\csc(\pi s) \int_0^\infty \left[}{1+a} ^\infty (1 + b_k a^k)\right] \; da = \pi^\infty ( (-1)^k + b_k)\csc(\pi s)