Paper: arXiv 2512.11666

Authors: Graham L Giller

Abstract

An analytical solution to single-horizon asset allocation for an investor with a piecewise-linear utility function, called herein the “budget threshold utility,” and exogenous position limits is presented. The resulting functional form has a surprisingly simple structure and can be readily interpreted as representing the addition of a simple “risk cost” to otherwise frictionless trading.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a heavy analytical derivation using advanced mathematical concepts like Gamma functions and generalized error distributions, but lacks empirical validation beyond theoretical discussion and a proposed constant for backtesting.

Research Flowchart

  flowchart TD
  A["Research Goal: Analytical solution for asset allocation<br>with budget threshold utility & position limits"] --> B["Methodology: Mean-Variance Optimization<br>with piecewise-linear utility constraints"]
  B --> C["Data Inputs: Asset return distributions<br>including leptokurtotic/fat-tailed"]
  C --> D["Computational Process: Derive first-order conditions<br>and solve for optimal portfolio weights"]
  D --> E["Key Finding: Simple analytical solution<br>representing risk cost added to frictionless trading"]
  E --> F["Outcome: Practical framework for<br>risk-limited asset allocation"]

Cited References (354)

  1. Nuclear Physics B. Nuclear Dynamics, Theoretical (1936) — link
  2. Zur Theorie der Kernmassen (1935) — link
  3. The Utility of Wealth in an Upper- and Lower-Partial Moment Fabric (2011) — link
  4. Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses (1989) — link
  5. The Variation of Certain Speculative Prices (1963) — link
  6. Survivorship Bias in Performance Studies (1992) — link
  7. Correlation without Factors in Retail Cryptocurrency Markets (2024) — link
  8. The Elements of Quantitative Investing (2025)
and 346 more
  1. MSCI USA Equity Factor Model (2025) — link
  2. A Five-Factor Asset Pricing Model (2015) — link
  3. CoinMarketCap (2013)
  4. Avalanche Platform (2020)
  5. Litecoin — a New Decentralized Currency (2011)
  6. Shiba Inu Ecosystem (2020)
  7. A Short History of Uniswap (2019)
  8. The Stellar Consensus Protocol: A Federated Model for Internet-level Consensus (2016)
  9. Tezos – A Self-Amending Crypto-Ledger (2018)
  10. Avalance Native Token ($AVAX) Dynamics (2020)
  11. Aave v3 Technical Paper (2022)
  12. Compound: The Money Market Protocol (2019)
  13. Dogecoin (2013)
  14. Chainlink 2.0: Next Steps in the Evolution of Decentralized Oracle Networks (2021)
  15. REST API Design Rulebook (2011)
  16. Isotropic Correlation Models for the Cross-Section of Equity Returns — → 2411.08864
  17. A Census of the Factor Zoo (2019)
  18. Foundations of Factor Investing (2013)
  19. Toward a Factor Structure in Crypto Asset Returns (2018)
  20. Factor Structure in Cryptocurrency Returns and Volatility (2019)
  21. Composite Leading Indicator and Cryptocurrency Returns: A Three-Factor Model (2024)
  22. Bitcoin: a Peer-to-Peer Electronic Cash System (2008)
  23. A Next-Generation Smart Contract and Decentralized Application Platform (2014)
  24. The Cross-Section of Expected Stock Returns (1992) — link
  25. Modern Factor Analysis (1976)
  26. Value and Momentum Everywhere (2013) — link
  27. Who Belongs in the Family? (1953) — link
  28. An Analytic Solution for Asset Allocation with a Multivariate Laplace Distribution (2024) — link
  29. Finance (2000)
  30. Array programming with NumPy (2020) — link
  31. Colab
  32. yfinance GitHub Repository (2019)
  33. Pandas (2020) — link
  34. D ata S tructures for S tatistical C omputing in P ython ( 2010 ) — link
  35. Python Tutorial (1995)
  36. The Arbitrage Theory of Capital Asset Pricing (2013)
  37. Linear Algebra Done Right (2015)
  38. It Turns out Other Countries Aren’t Normal Either (2024) — link
  39. Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH (2001)
  40. C APITAL A SSET P RICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK (1964) — link
  41. On Modeling and Interpreting the Economics of Catastrophic Climate Change (2009)
  42. The Theory of Risk Aversion (1971)
  43. A Critique of Expected Utility Theory: Descriptive and Normative Considerations (1975)
  44. Expected utility theory (2007)
  45. Thinking Differently About Asset Allocation (2023) — link
  46. Triumph of the Optimists : 101 Years of Global Investment Returns (2002) — link
  47. Computing the Two-Sided Kolmogorov-Smirnov Distribution (2011) — link
  48. Nonparametric Goodness-of-Fit Tests for Discrete Null Distributions (2011) — link
  49. \texttt arch (2023)
  50. rally \textit int.verb (1) (2023)
  51. Comparing Sharpe Ratios : so where are the $p$-values? (2007)
  52. A Demon of Our Own Design : Markets, hedge funds, and the perils of financial innovation (2007)
  53. Let’s Just Eliminate the Variance (2009)
  54. Matrix Algebra from a Statistician’s Perspective (1998)
  55. \textit GitHub Repository (2022)
  56. Gunnar Myrdal: An Intellectual Biography (2008)
  57. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python (2020) — link
  58. Counterfactuals (2021)
  59. Adventures in Financial Data Science: The Empirical Properties of Financial and Economic Data (2022)
  60. Two Conjectures on Capital Placed at Risk (2022) — link
  61. The Sharpe Ratio is a Terrible Statistic to Use to Optimize Trading Strategies (2023) — link
  62. When Building Alphas, Should we Do the Right Thing? (2023) — link
  63. Yes, Quants Should Care about Money Left on the Table (2023)
  64. Invesco QQQ Trust\textsuperscript SM , Series 1 (2022)
  65. SPDR\textregistered\ Dow Jones\textregistered\ Industrial Average ETF Trust (2022)
  66. SPDR\textregistered\ S&P 500\textregistered\ ETF Trust (2022)
  67. Partial Correlation (2022) — link
  68. List of S&P 500 Companies (2024) — link
  69. The New Market Wizards: Conversations with America’s Top Traders (2012)
  70. Particle Physics Booklet (2010)
  71. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (2020)
  72. T HE N ORMAL D ISTRIBUTION D OESN’T W ORK, IT’S T IME TO S TOP U SING IT! (2022) — link
  73. Mental Accounting and Consumer Choice (1985)
  74. The Complete Memoirs of Jacques Casanova (2004)
  75. Option Pricing : mathematical models and computation (1993)
  76. 2003 Nobel Price Lecture: Time Series Analysis, Cointegration, and Applications (2003)
  77. Your Possible Pasts (1983)
  78. Frictionless Asset Allocation with Elliptically Symmetric Distributions of Returns (2004)
  79. A Man for All Markets: from Las Vegas to Wall Street, How I Beat the Dealer and the Market (2017)
  80. Principles of Corporate Finance (2018)
  81. \texttt arch Python package (2021)
  82. Some Aspects of Statistical Design in Quality Improvement (1987) — link
  83. Conditional Heteroskedasticity in Asset Returns: A new approach (1991)
  84. On the Mathematical Foundations of Theoretical Statistics (1922) — link
  85. Statistics Review 8: Qualitative Data–Tests of Association (2003)
  86. Quantum Mechanics (1965)
  87. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles (1985)
  88. The Theory of Probability (1998)
  89. The Kendall Rank Correlation Coefficient (2007)
  90. The Distribution of Kendall’s tau for Testing the Significance of Cross-correlation in Persistent Data (2011)
  91. Graphs in Statistical Analysis (1973)
  92. Robust Statistics (2004)
  93. Applied Regression Analysis (1998)
  94. Statistics, 4th.\ Edition (2007)
  95. Python 3 Reference Manual (2009)
  96. Data Structures for Statistical Computing in Python (2010)
  97. The Econometrics of Financial Markets (2012)
  98. Bloomberg L.P.: About, products, contacts (2022)
  99. Correlation at Scale: Analysis of BI Dashboards (2021–2022)
  100. A Thermionic Trigger (1938)
  101. Perceptrons: An introduction to computational geometry (2017)
  102. Boolean Algebra and its Applications (2012)
  103. Approximation by Superpositions of a Sigmoidal Function (1989)
  104. Multilayer Feedforward Networks are Universal Approximators (1989)
  105. Risk Aversion in the Small and in the Large (1964)
    1. Market Microstructure (2012)
  107. McGraw-Hill’s Dictionary of American Idioms and Phrasal Verbs (2007)
  108. Essays on Trading Strategy (Expected 2023)
  109. Essays on Trading Strategy (2023)
  110. Th 'e orie de la sp 'e culation (1900)
  111. One In Ten (1981)
  112. The Adventures of a Modern Renaissance Academic in Investing and Gambling (2017)
  113. Problems in Portfolio Theory and the Fundamentals of Financial Decision Making (2017)
  114. Transactions costs, extent of inefficiencies, entries and multiple wagers in a racetrack betting model (2011)
  115. Disinformation, misinformation and inequality-driven mistrust in the time of COVID-19: lessons unlearned from AIDS denialism (2020)
  116. 2020 Electoral College Results (2021)
  117. A contribution to the mathematical theory of epidemics (1927)
  118. Prediction of confirmed cases of and deaths caused by COVID-19 in Chile through time series techniques: A comparative study (2021)
  119. FDA Takes Key Action in Fight Against COVID-19 By Issuing Emergency Use Authorization for First COVID-19 Vaccine (2020)
  120. An Interview with George B. Dantzig: The Father of Linear Programming (1986)
  121. The Art of Electronics (1989)
  122. The nature of statistical learning theory (2013)
  123. Mathematical methods for Physicists (1985)
  124. Private communication
  125. Exposition of a New Theory on the Measurement of Risk (1954)
  126. Kendall’s Advanced Theory of Statistics (1999)
  127. Kendall’s Advanced Theory of Statistics (1999)
  128. Kendall’s Advanced Theory of Statistics (1999)
  129. The Statistics of Sharpe Ratios (2002)
  130. Approximate Statistical Properties of the Sharpe Ratio (1997)
  131. Proprietary trading: truth and fiction (2001)
  132. Mental Accounting and Consumer Choice (2008) — link
  133. Beat the Dealer: a winning strategy for the game of twenty one (1966)
  134. The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market (2011)
  135. A New Interpretation of the Information Rate (1956) — link
  136. A New Interpretation of the Information rate (2011)
  137. The Capital Asset Pricing Model: Theory and Evidence (2004) — link
  138. Multiperiod Portfolio Selection and Bayesian Dynamic Models (2014)
  139. Option pricing: A simplified approach (1979)
  140. Introduction to Stochastic Programming (2011)
  141. Crossover from Linear to Square-Root Market Impact (2019)
  142. Master Curve for Price-Impact Function (2003)
  143. The London Whale (2018)
  144. When genius failed: The rise and fall of Long-Term Capital Management (2000)
  145. Portfolio Theory and Investment Management (1994)
  146. Adventures in Financial Data Science: The empirical properties of financial data and some other things that interested me… (2020)
  147. The present-day star formation rate of the Milky Way determined from Spitzer-detected young stellar objects (2010)
  148. Results from a dozen years of election futures markets research (2008)
  149. The promise of prediction markets (2008)
  150. The futures game: who wins? Who loses? Why? (1989)
  151. Understanding Uncertainty (2013)
  152. Information theory and statistics (1997)
  153. Elements of Information Theory John Wiley & Sons (1991)
  154. Elements of information theory second edition solutions to problems (2006)
  155. The Drake equation revisited: part I (2003)
  156. Is anyone out there (1992)
  157. Minimization of the kullback–leibler divergence for nonlinear estimation (2017)
  158. On the distributional transform, Sklar’s theorem, and the empirical copula process (2009) — link
  159. ``Where is everybody?’’ An Account of Fermi’s Question (1985)
  160. Dissolving the Fermi Paradox (2018) — link
  161. A New Characterization of the Dirichlet Distribution through Neutrality (1980)
  162. Concepts of independence for proportions with a generalization of the Dirichlet distribution (1969)
  163. Choosing a point from the surface of a sphere (1972)
  164. Encyclopedic dictionary of mathematics (1993)
  165. Portfolio Selection (1952)
  166. A multivariate Kolmogorov-Smirnov test of goodness of fit (1997)
  167. The Advanced Theory of Statistics. Vol. 1. (1948)
  168. Tables of Integrals, etc. (1965)
  169. The Construction and Properties of Ellipsoidal Probability Density Functions (2003)
  170. The statistical properties of random bitstreams and the sampling distribution of cosine similarity (2012)
  171. Beyond market baskets: Generalizing association rules to dependence rules (1998)
  172. Graham Giller: S.S.R.N. Author Page (2020)
  173. Practical methods of optimization (2013)
  174. Finding and evaluating community structure in networks (2004)
  175. Google’s PageRank and beyond: The science of search engine rankings (2011)
  176. County Adjacencies File (2020)
  177. Presidential Approval by State (2020)
  178. Statement on the first meeting of the International Health Regulations (2005) Emergency Committee regarding the outbreak of novel coronavirus (2019-nCoV) (2020)
  179. COVID-19 Dashboard (2020)
  180. Executive Order 107 (2020)
  181. Modeling COVID-19 Across the United States (2020)
  182. Generalized Autoregressive Dirichlet Multinomial Models: Definition and Stability (2020)
  183. On the rate of gain of information (1952)
  184. Animal spirits: How human psychology drives the economy, and why it matters for global capitalism (2010)
  185. Surveys of Consumers: Summary (2020)
  186. Surveys of Consumers: Questionnaire (2020)
  187. CART: classification and regression trees (2009)
  188. The Mathematical Theory of Communication (1962)
  189. Short texts, best-fitting curves and new measures of lexical diversity (2002)
  190. Farewell Etaoin Shrdlu: An Age-Old Printing Process Gives Way to Modern Technology (1983)
  191. Natural language processing with Python: analyzing text with the natural language toolkit (2009)
  192. Further Beyond Zipf’s Law: A Quadratic Model for the Frequency-Rank Distribution for the Brown Corpus and Other Commonly Available English Corpora (2013)
  193. Fractals and scaling in finance: Discontinuity, concentration, risk. Selecta volume E (2013)
  194. The fractal geometry of nature/Revised and enlarged edition (1983)
  195. Random texts exhibit Zipf’s-law-like word frequency distribution (1992)
  196. George Kingsley Zipf: life, ideas, his law and informetrics. (2002)
  197. Selected Studies of the Principle of Relative Frequency in Language (1932)
  198. Good calories, bad calories (2007)
  199. Adolphe Quetelet (1796–1874)—the average man and indices of obesity (2008)
  200. The mysterious trend in American heights in the 20th century (2007)
  201. The formula that killed Wall Street (2012)
  202. A Probit Model for Presidential Elections in Terms of Relative Height and Desire for Change (2012)
  203. The Dantzig selector: Statistical estimation when p is much larger than n (2007)
  204. The Myth of the Rational Voter: Why Democracies Choose Bad Policies-New Edition (2011)
  205. The Measure of a President (2008) — link
  206. Active Portfolio Management (2000)
  207. Time Series Analysis (1994)
  208. On the anomalous acceleration of 1I/2017 U1 `Oumuamua (2019)
  209. The five ages of the universe: inside the physics of eternity (2016)
  210. Statistical Distributions (2011)
  211. Handbook of econometrics (1983)
  212. Statistical methods in experimental physics (2006)
  213. The Accuracy of Autoregressive Forecasts of the Average Monthly Temperatures in Central England, Central Park and New Jersey (2013)
  214. Efficiency of racetrack betting markets (2008)
  215. Five years of LEP experiments (1995)
  216. Tail probabilities for the null distribution of scanning statistics (2000)
  217. The approximate distribution of the maximum of a smoothed Poisson random field (1997)
  218. Complexity in crisis: The volcanic cold pulse of the 1690s and the consequences of Scotland’s failure to cope (2020)
  219. The Construction and Analysis of a Whole-Sky Map Using Underground Muons (1994)
  220. A seasonal autoregressive model for the Central England temperature series (2012)
  221. Nonparametric regression and generalized linear models: a roughness penalty approach (1993)
  222. The winter of discontent thirty years on (2009)
  223. Monthly Mean Central England Temperature, 1659-1973 (1974)
  224. Analysis of Panel Data (2014)
  225. Consumer expectations: Micro foundations and macro impact (2019)
  226. V ox P opuli (1907)
  227. Maximum likelihood estimation of a poissonian count rate function for the followers of a twitter account making directional forecasts of the stock market (2009)
  228. The sign of four (2010)
  229. Model Selection and Multimodel Inference (2002)
  230. The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses (1938)
  231. The incredible Volcker disinflation (2005)
  232. Mathematical Approach to Biology and Medicine (1967)
  233. Mathematical Approach to Biology and Medicine (1967)
  234. Dark pools: High-speed traders, AI bandits, and the threat to the global financial system (2012)
  235. Flash boys: a Wall Street revolt (2014)
  236. Modelling volatility mean reversion in stock market prices: Implications for long-term investment (2016)
  237. More than you ever wanted to know about volatility swaps (1999)
  238. The Jackknife, the Bootstrap and Other Resampling Plans (1982)
  239. Options, Futures and Other Derivatives (2009)
  240. The Founders of Modern Finance: their prize-winning concepts and 1990 Nobel lectures (1991)
  241. Continuous Auctions and Insider Trading (1985)
  242. A new notation for quantum mechanics (1939)
  243. Risk, return, and equilibrium: Empirical tests (1973)
  244. `` S ometimes it’s just random.’’ (1999)
  245. The Quants: How a new breed of math whizzes conquered Wall Street and nearly destroyed it (2010)
  246. The Man who Solved the Market: How Jim Simons Launched the Quant Revolution (2019)
  247. Maximum Likelihood for Social Science: Strategies for Analysis (2018)
  248. The Oxford dictionary of statistical terms (2006)
  249. Econometric analysis (2003)
  250. The Design of Experiments (1960)
  251. ``In machine learning these methods aren’t relevant.’’ (2016)
  252. On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks (1993)
  253. M aria is no longer sweet on ’ H oney’ (2010)
  254. `` A ll alphas are betas onto risk factors not yet named’’ (1998)
  255. Federal Reserve Issues FOMC Statement (2015)
  256. The Pricing of Options and Contingent Claims (1973)
  257. The Imitation Game (2014)
  258. The Spider Network: The Wild Story of a Maths Genius, a Gang of Backstabbing Bankers, and One of the Greatest Scams in Financial History (2017)
  259. Probability and Random Processes (1992)
  260. Statistical Methods in Markov Chains (1960)
  261. A theory of the term structure of interest rates (2005)
  262. An equilibrium characterization of the term structure (1977)
  263. RISK AND VOLATILITY: ECONOMETRIC MODELS AND FINANCIAL PRACTICE RISK AND VOLATILITY: ECONOMETRIC MODELS AND FINANCIAL PRACTICE RISK AND VOLATILITY: ECONOMETRIC MODELS AND FINANCIAL PRACTICE Risk and V olatility: Econometric Models and Financial Practice (2003)
  264. Short-Rate Models (2020) — link
  265. Liar’s Poker (2010)
  266. The handbook of fixed income securities (2012)
  267. A history of interest rates (1996)
  268. Zero bound on interest rates and optimal monetary policy (2003)
  269. The Kolmogorov-Smirnov test for goodness of fit (1951)
  270. Large sample estimation and hypothesis testing, Ch. 36 in Handbook of econometrics, vol. 4, RF Engle and D. McFadden eds (1994)
  271. Frequency D istribution of the V alues of the C orrelation C oefficient in S amples of an I ndefinitely L arge P opulation (1915)
  272. The N ifty- F ifty R e- R evisited (2002)
  273. Efficient C apital M arkets: A review of theory and empirical work (1970)
  274. On P ersistence in M utual F und P erformance (1997)
  275. Autoregressive C onditional H eteroscedasticity with E stimates of the V ariance of I nflationary E xpectations (1979)
  276. Jarque-Bera T est and its C ompetitors for T esting N ormality—a P ower C omparison (2007)
  277. Stocks for the L ong R un (1998)
  278. A Generalized Error Distribution (2005)
  279. Continuous Time Finance (1992)
  280. Investigations on the Theory of the Brownian Movement (1956)
  281. Statistics for E xperimenters (1978)
  282. Electronics: P rinciples and A pplications (1991)
  283. Google S cholar Profile Page (2020) — link
  284. Deep t hinking: where machine intelligence ends and human creativity begins (2017)
  285. The Pleasure of Finding Things Out: the best short works of Richard P. Feynman (2005)
  286. Stochastic V olatility: S elected R eadings (2005)
  287. GARCH 101 : The use of ARCH/GARCH M odels in A pplied E conometrics (2001)
  288. G eneralized L inear M odels (1972)
  289. H andbook of M athematical F unctions (1970)
  290. A N ote on the D elta M ethod (1992)
  291. Multivariate A nalysis (1979)
  292. On the C ompound M ultinomial D istribution, the M ultivariate $\beta$-distribution, and C orrelations A mong P roportions (1962)
  293. Analysis of the H uman S ex R atio by using O verdispersion M odels (1998)
  294. Forecasting, S tructural T ime S eries M odels and the K alman F ilter (1990)
  295. Time Series Analysis: Forecasting and Control (2015)
  296. How P opular/ U npopular is D onald T rump? (2019)
  297. How W e’re T racking D onald T rump’s A pproval R atings (2017)
  298. M onmouth U niversity P oll (2019)
  299. A S imple S urvey of E mployment S tatus and F uture E xpectations (2018)
  300. G eneralized A utoregressive C onditional H eteroskedasticity (1986) — link
  301. A utoregressive C onditional H eteroscedasticity with E stimates of the V ariance of U nited K ingdom I nflation (1982) — link
  302. Time Series Analysis by State Space Methods (2012)
  303. The X-13A-S Seasonal Adjustment Program (2009)
  304. Current Population Survey Handbook of Methods (2018)
  305. Current Population Survey Technical Paper 66 (2006)
  306. Current Employment Statistics
  307. Confidence Intervals from the Rayleigh test (1994)
  308. Betting and Equalibrium (2008) — link
  309. Market Efficiency, Long-Term Returns, and Behavioral Finance (1998) — link
  310. Behavioural Risk Factor Surveillance System, 2012 (2013)
  311. How Google Surveys Works (2017)
  312. American Fact Finder (2018)
  313. Vox Populi (1907) — link
  314. On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known (1940) — link
  315. Thinking, Fast and Slow (2011) — link
  316. Modern Mental Chronometry (1988) — link
  317. On the Rate of Gain of Information (1952) — link
  318. Weighted median algorithms for $L_1$ approximation (1990) — link
  319. 2010 Decenial Census, Summary File 1 (2013)
  320. Consumer Price Indices (current)
  321. Presidential Approval Ratings (2009–date)
  322. Compressed Sensing: Robust Recovery of Sparse Signals from Limited Measurements (2008) — link
  323. A Simplex Method for Function Minimization (1965) — link
  324. A Family of Variable Metric Updates Derived by Variational Means (1970) — link
  325. Frequency Distribution of the Values of the Correlation Coefficient in Samples of an Indefinitely Large Population (1915)
  326. RATS Version 10: Reference Manual (2020)
  327. A New Polynomial Time Algorithm for Linear Programming (1984)
  328. Linear Programming (1983)
  329. Perceptrons: An Introduction to Computational Geometry (1969)
  330. Contour Enhancement, Short Term Memory, and Constancies in Reverberating Neural Networks (1973)
  331. The Nature of Statistical Learning Theory (1999)
  332. Neural Networks for Pattern Recognition (1995)
  333. Global-scale temperature patterns and climate forcing over the past six centuries (1998)
  334. CORRECTIONS TO THE \textrm Mann et. al. (1998) PROXY DATA BASE AND NORTHERN HEMISPHERIC AVERAGE TEMPERATURE SERIES (2003)
  335. MONTHLY MEAN CENTRAL ENGLAND TEMPERATURE (DEGREES \textrm C ) 1974– (1992)
  336. MONTHLY MEAN CENTRAL ENGLAND TEMPERATURE (DEGREES \textrm C ) 1974– (2005)
  337. The Central England Temperature Series (Degrees \textrm C ) 1659–date (updated monthly)
  338. Training of Working Memory in Children with ADHD (2002)
  339. Computerized Training of Working Memory in Children With ADHD —A Randomized, Controlled Trial (2005)
  340. Cogmed Working Memory Training
  341. Cogmed RM
  342. Changes in cortical activity after training of working memory —- a single-subject analysis (2007)
  343. Working-memory training in younger and older adults: training gains, transfer, and maintenance. (2012)
  344. Statistical Methods in Experimental Physics (1971)
  345. The generalization of `` S tudent’s’’ problem when several different population variances are involved (1947)
  346. Scaling up top-$K$ cosine similarity search (2011)

1 of 354 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.