pwc-archive/papers-with-abstracts huggingface dataset:
Topological Data Analysis of Biological Aggregation Models
Date: 2015-03-11 00:00:00
Tasks: Topological Data Analysis

We apply tools from topological data analysis to two mathematical models
inspired by biological aggregations such as bird flocks, fish schools, and
insect swarms. Our data consists of numerical simulation output from the models
of Vicsek and D'Orsogna. These models are dynamical systems describing the
movement of agents who interact via alignment, attraction, and/or repulsion.
Each simulation time frame is a point cloud in position-velocity space. We
analyze the topological structure of these point clouds, interpreting the
persistent homology by calculating the first few Betti numbers. These Betti
numbers count connected components, topological circles, and trapped volumes
present in the data. To interpret our results, we introduce a visualization
that displays Betti numbers over simulation time and topological persistence
scale. We compare our topological results to order parameters typically used to
quantify the global behavior of aggregations, such as polarization and angular
momentum. The topological calculations reveal events and structure not captured
by the order parameters.
Stationary solutions for metapopulation Moran models with mutation and selection
Date: 2015-04-14 00:00:00

We construct an individual-based metapopulation model of population genetics
featuring migration, mutation, selection and genetic drift. In the case of a
single `island', the model reduces to the Moran model. Using the diffusion
approximation and timescale separation arguments, an effective one-variable
description of the model is developed. The effective description bears
similarities to the well-mixed Moran model with effective parameters which
depend on the network structure and island sizes, and is amenable to analysis.
Predictions from the reduced theory match the results from stochastic
simulations across a range of parameters. The nature of the fast-variable
elimination technique we adopt is further studied by applying it to a linear
system, where it provides a precise description of the slow-dynamics in the
limit of large timescale separation.
Evolutionary Dynamics with Fluctuating Population Sizes and Strong Mutualism
Date: 2016-08-29 00:00:00

Game theory ideas provide a useful framework for studying evolutionary
dynamics in a well-mixed environment. This approach, however, typically
enforces a strictly fixed overall population size, deemphasizing natural growth
processes. We study a competitive Lotka-Volterra model, with number
fluctuations, that accounts for natural population growth and encompasses
interaction scenarios typical of evolutionary games. We show that, in an
appropriate limit, the model describes standard evolutionary games with both
genetic drift and overall population size fluctuations. However, there are also
regimes where a varying population size can strongly influence the evolutionary
dynamics. We focus on the strong mutualism scenario and demonstrate that
standard evolutionary game theory fails to describe our simulation results. We
then analytically and numerically determine fixation probabilities as well as
mean fixation times using matched asymptotic expansions, taking into account
the population size degree of freedom. These results elucidate the interplay
between population dynamics and evolutionary dynamics in well-mixed systems.
Public good diffusion limits microbial mutualism
Date: 2015-05-23 00:00:00

Standard game theory cannot describe microbial interactions mediated by
diffusible molecules. Nevertheless, we show that one can still model microbial
dynamics using game theory with parameters renormalized by diffusion. Contrary
to expectations, greater sharing of metabolites reduces the strength of
cooperation and leads to species extinction via a nonequilibrium phase
transition. We report analytic results for the critical diffusivity and the
length scale of species intermixing. We also show that fitness nonlinearities
suppress mutualism and favor the species producing slower nutrients.
Large-scale empirical study on pairs trading for all possible pairs of stocks listed on the first section of the Tokyo Stock Exchange
Date: 2015-03-19 00:00:00
Tasks: All, Asset Management, Management

We carry out a large-scale empirical data analysis to examine the efficiency
of the so-called pairs trading. On the basis of relevant three thresholds,
namely, starting, profit-taking, and stop-loss for the `first-passage process'
of the spread (gap) between two highly-correlated stocks, we construct an
effective strategy to make a trade via `active' stock-pairs automatically. The
algorithm is applied to $1,784$ stocks listed on the first section of the Tokyo
Stock Exchange leading up to totally $1,590,436$ pairs. We are numerically
confirmed that the asset management by means of the pairs trading works
effectively at least for the past three years (2010-2012) data sets in the
sense that the profit rate becomes positive (totally positive arbitrage) in
most cases of the possible combinations of thresholds corresponding to
`absorbing boundaries' in the literature of first-passage processes.
A Simulation for Neurophotonic Quantum Computation in Visual Pathways
Date: 2015-04-17 00:00:00

One of the answers to the measurement problem in quantum theory is given by
the Copenhagen-Interpretation of quantum theory (i.e. orthodox quantum theory)
in which the wave function collapse happens in (by) the mind of observer. In
fact, at first, great scientists like Von Neumann, London, Bauer and Wigner
(initially) believed that the wave function collapse occurs in the brain or is
caused by the consciousness of observer. However, this issue has been stayed
yet very controversial. In fact, there are many challenging discussions about
the survival of quantum effects in microscopic structures of the human brain,
which is mainly because of quick decoherence of quantum states due to hot, wet
and noisy environment of the brain that forbids long life coherence for brain
processing. Nevertheless, there are also several arguments and evidences that
emergence of large coherent states is feasible in the brain. In this paper, our
approach is based on the latter in which macroscopic quantum states are
probable in the human brain. Here, we simulate the delayed luminescence of
photons in neurons with a Brassard-like teleportation circuit, i.e. equivalent
to the transfer of quantum states of photons through the visual pathways from
retina to the visual cortex. Indeed, our simulation considers both classical
and quantum mechanical aspects of processing in neurons. As a result and based
on our simulation, it is possible for our brain to receive the exact quantum
states of photons in the visual cortex to be collapsed by our consciousness,
which supports the Copenhagen-Interpretation of measurement problem in quantum
theory.
A new perspective on the fundamental theorem of asset pricing for large financial markets
Authors: Christa Cuchiero, Irene Klein, Josef Teichmann
Date: 2014-12-23 00:00:00

In the context of large financial markets we formulate the notion of \emph{no asymptotic free lunch with vanishing risk} (NAFLVR), under which we can prove a version of the fundamental theorem of asset pricing (FTAP) in markets with an (even uncountably) infinite number of assets, as it is for instance the case in bond markets. We work in the general setting of admissible portfolio wealth processes as laid down by Y. Kabanov \cite{kab:97} under a substantially relaxed concatenation property and adapt the FTAP proof variant obtained in \cite{CT:14} for the classical small market situation to large financial markets. In the case of countably many assets, our setting includes the large financial market model considered by M. De Donno et al. \cite{DGP:05} and its abstract integration theory. The notion of (NAFLVR) turns out to be an economically meaningful "no arbitrage" condition (in particular not involving weak-$*$-closures), and, (NAFLVR) is equivalent to the existence of a separating measure. Furthermore we show -- by means of a counterexample -- that the existence of an equivalent separating measure does not lead to an equivalent $\sigma$-martingale measure, even in a countable large financial market situation.
Relation between firing statistics of spiking neuron with instantaneous feedback and without feedback
Date: 2015-02-12 00:00:00
Tasks: Relation

We consider a wide class of spiking neuron models, defined by rather general
set of conditions typical for basic models like leaky integrate and fire, or
binding neuron model. A neuron is fed with a point renewal process. A relation
between the three probability density functions (pdf): (i) pdf of input
interspike intervals, (ii) pdf of output interspike intervals of a neuron with
instantaneous feedback and (iii) pdf for that same neuron without feedback is
derived. This allows to calculate any of the three pdfs provided the another
two are given. Similar relation between corresponding means and variances is
derived. The relations are checked exactly for the binding neuron model.
Adaptive Market Efficiency of Agricultural Commodity Futures Contracts
Date: 2015-03-31 00:00:00

In this paper we investigate the adaptive market efficiency of the
agricultural commodity futures market, using a sample of eight futures
contracts. Using a battery of nonlinear tests, we uncover the nonlinear serial
dependence in the returns series. We run the Hinich portmanteau bicorrelation
test to uncover the moments in which the nonlinear serial dependence, and
therefore adaptive market efficiency, occurs for our sample.
Optimal Digital Product Maintenance with a Continuous Revenue Stream
Date: 2017-02-25 00:00:00

We use a control framework to analyze the digital vendor's profit
maximization problem. The vendor captures market share by focusing costly
effort on post-launch product maintenance, which influences user perception of
the product and drives a revenue stream associated with product use. Our
theoretical results show necessary and sufficient conditions for product
maintenance to decline over a product's life-cycle, thus showing conditions
when Lehman's 7th law of software evolution holds. We also numerically
illustrate control paths under different market conditions.
On the spot-futures no-arbitrage relations in commodity markets
Date: 2018-02-24 00:00:00

In commodity markets the convergence of futures towards spot prices, at the
expiration of the contract, is usually justified by no-arbitrage arguments. In
this article, we propose an alternative approach that relies on the expected
profit maximization problem of an agent, producing and storing a commodity
while trading in the associated futures contracts. In this framework, the
relation between the spot and the futures prices holds through the
well-posedness of the maximization problem. We show that the futures price can
still be seen as the risk-neutral expectation of the spot price at maturity and
we propose an explicit formula for the forward volatility. Moreover, we provide
an heuristic analysis of the optimal solution for the
production/storage/trading problem, in a Markovian setting. This approach is
particularly interesting in the case of energy commodities, like electricity:
this framework indeed remains suitable for commodities characterized by
storability constraints, when standard no-arbitrage arguments cannot be safely
applied.
An Event-Driven Approach for Studying Gene Block Evolution in Bacteria
Date: 2015-02-24 00:00:00
Tasks: Open-Ended Question Answering

Motivation: Gene blocks are genes co-located on the chromosome. In many
cases, genes blocks are conserved between bacterial species, sometimes as
operons, when genes are co-transcribed. The conservation is rarely absolute:
gene loss, gain, duplication, block splitting, and block fusion are frequently
observed. An open question in bacterial molecular evolution is that of the
formation and breakup of gene blocks, for which several models have been
proposed. These models, however, are not generally applicable to all types of
gene blocks, and consequently cannot be used to broadly compare and study gene
block evolution. To address this problem we introduce an event-based method for
tracking gene block evolution in bacteria. Results: We show here that the
evolution of gene blocks in proteobacteria can be described by a small set of
events. Those include the insertion of genes into, or the splitting of genes
out of a gene block, gene loss, and gene duplication. We show how the
event-based method of gene block evolution allows us to determine the
evolutionary rate, and to trace the ancestral states of their formation. We
conclude that the event-based method can be used to help us understand the
formation of these important bacterial genomic structures. Availability: The
software is available under GPLv3 license on
http://github.com/reamdc1/gene_block_evolution.git Supplementary online
material: http://iddo-friedberg.net/operon-evolution Contact: Iddo Friedberg
i.friedberg@miamioh.edu
Quantum Cognition based on an Ambiguous Representation Derived from a Rough Set Approximation
Date: 2015-11-19 00:00:00
Tasks: Decision Making

Over the last years, in a series papers by Arrechi and others, a model for
the cognitive processes involved in decision making has been proposed and
investigated. The key element of this model is the expression of apprehension
and judgement, basic cognitive process of decision making, as an inverse Bayes
inference classifying the information content of neuron spike trains. For
successive plural stimuli, it has been shown that this inference, equipped with
basic non-algorithmic jumps, is affected by quantum-like characteristics. We
show here that such a decision making process is related consistently with
ambiguous representation by an observer within a universe of discourse. In our
work ambiguous representation of an object or a stimuli is defined by a pair of
maps from objects of a set to their representations, where these two maps are
interrelated in a particular structure. The a priori and a posteriori
hypotheses in Bayes inference are replaced by the upper and lower
approximation, correspondingly, for the initial data sets each derived with
respect to a map. We show further that due to the particular structural
relation between the two maps, the logical structure of such combined
approximations can only be expressed as an orthomodular lattice and therefore
can be represented by a quantum rather than a Boolean logic. To our knowledge,
this is the first investigation aiming to reveal the concrete logic structure
of inverse Bayes inference in cognitive processes.
Monetary Policy and Dark Corners in a stylized Agent-Based Model
Date: 2016-01-12 00:00:00
Tasks: Navigate

We extend in a minimal way the stylized model introduced in in "Tipping
Points in Macroeconomic Agent Based Models" [JEDC 50, 29-61 (2015)], with the
aim of investigating the role and efficacy of monetary policy of a `Central
Bank' that sets the interest rate such as to steer the economy towards a
prescribed inflation and employment level. Our major finding is that provided
its policy is not too aggressive (in a sense detailed in the paper) the Central
Bank is successful in achieving its goals. However, the existence of different
equilibrium states of the economy, separated by phase boundaries (or "dark
corners"), can cause the monetary policy itself to trigger instabilities and be
counter-productive. In other words, the Central Bank must navigate in a narrow
window: too little is not enough, too much leads to instabilities and wildly
oscillating economies. This conclusion strongly contrasts with the prediction
of DSGE models.
Modeling the ballistic-to-diffusive transition in nematode motility reveals variation in exploratory behavior across species
Date: 2019-03-24 00:00:00

A quantitative understanding of organism-level behavior requires predictive
models that can capture the richness of behavioral phenotypes, yet are simple
enough to connect with underlying mechanistic processes. Here we investigate
the motile behavior of nematodes at the level of their translational motion on
surfaces driven by undulatory propulsion. We broadly sample the nematode
behavioral repertoire by measuring motile trajectories of the canonical lab
strain $C. elegans$ N2 as well as wild strains and distant species. We focus on
trajectory dynamics over timescales spanning the transition from ballistic
(straight) to diffusive (random) movement and find that salient features of the
motility statistics are captured by a random walk model with independent
dynamics in the speed, bearing and reversal events. We show that the model
parameters vary among species in a correlated, low-dimensional manner
suggestive of a common mode of behavioral control and a trade-off between
exploration and exploitation. The distribution of phenotypes along this primary
mode of variation reveals that not only the mean but also the variance varies
considerably across strains, suggesting that these nematode lineages employ
contrasting ``bet-hedging'' strategies for foraging.
Graph Theoretical Analysis Reveals: Women's Brains are Better Connected than Men's
Date: 2015-01-12 00:00:00
Tasks: Diffusion  MRI

Deep graph-theoretic ideas in the context with the graph of the World Wide
Web led to the definition of Google's PageRank and the subsequent rise of the
most-popular search engine to date. Brain graphs, or connectomes, are being
widely explored today. We believe that non-trivial graph theoretic concepts,
similarly as it happened in the case of the World Wide web, will lead to
discoveries enlightening the structural and also the functional details of the
animal and human brains. When scientists examine large networks of tens or
hundreds of millions of vertices, only fast algorithms can be applied because
of the size constraints. In the case of diffusion MRI-based structural human
brain imaging, the effective vertex number of the connectomes, or brain graphs
derived from the data is on the scale of several hundred today. That size
facilitates applying strict mathematical graph algorithms even for some
hard-to-compute (or NP-hard) quantities like vertex cover or balanced minimum
cut. In the present work we have examined brain graphs, computed from the data
of the Human Connectome Project, recorded from male and female subjects between
ages 22 and 35. Significant differences were found between the male and female
structural brain graphs: we show that the average female connectome has more
edges, is a better expander graph, has larger minimal bisection width, and has
more spanning trees than the average male connectome. Since the average female
brain weights less than the brain of males, these properties show that the
female brain is more "well-connected" or perhaps, more "efficient" in a sense
than the brain of males.
The Temporal Dimension of Risk
Date: 2016-06-27 00:00:00

Multi-period measures of risk account for the path that the value of an
investment portfolio takes. In the context of probabilistic risk measures, the
focus has traditionally been on the magnitude of investment loss and not on the
dimension associated with the passage of time. In this paper, the concept of
temporal path-dependent risk measure is mathematically formalized to capture
the risk associated with the temporal dimension of a stochastic process. We
discuss the properties of temporal measures of risk and show that they can
never be coherent. We then study the temporal dimension of investment drawdown,
its duration, which measures the length of excursions below a running maximum.
Its properties in the context of risk measures are analyzed both theoretically
and empirically. In particular, we show that duration captures serial
correlation in the returns of two major asset classes. We conclude by
discussing the challenges of path-dependent temporal risk estimation in
practice.
Shortfall Deviation Risk: An alternative to risk measurement
Date: 2016-05-10 00:00:00

We present the Shortfall Deviation Risk (SDR), a risk measure that represents
the expected loss that occurs with certain probability penalized by the
dispersion of results that are worse than such an expectation. SDR combines
Expected Shortfall (ES) and Shortfall Deviation (SD), which we also introduce,
contemplating two fundamental pillars of the risk concept, the probability of
adverse events and the variability of an expectation, and considers extreme
results. We demonstrate that SD is a generalized deviation measure, whereas SDR
is a coherent risk measure. We achieve the dual representation of SDR, and we
discuss issues such as its representation by a weighted ES, acceptance sets,
convexity, continuity and the relationship with stochastic dominance.
Illustrations with real and simulated data allow us to conclude that SDR offers
greater protection in risk measurement compared with VaR and ES, especially in
times of significant turbulence in riskier scenarios.
Response of polygenic traits under stabilising selection and mutation when loci have unequal effects
Date: 2016-01-12 00:00:00

We consider an infinitely large population under stabilising selection and
mutation in which the allelic effects determining a polygenic trait vary
between loci. We obtain analytical expressions for the stationary genetic
variance as a function of the distribution of effects, mutation rate and
selection coefficient. We also study the dynamics of the allele frequencies,
focussing on short-term evolution of the phenotypic mean as it approaches the
optimum after an environmental change. We find that when most effects are
small, the genetic variance does not change appreciably during adaptation, and
the time until the phenotypic mean reaches the optimum is short if the number
of loci is large. However, when most effects are large, the change of the
variance during the adaptive process cannot be neglected. In this case, the
short-term dynamics may be described by that of a single locus of large effect.
Our results may be used to understand polygenic selection driving rapid
adaptation.
The Golden Target: Analyzing the Tracking Performance of Leveraged Gold ETFs
Date: 2015-01-22 00:00:00

This paper studies the empirical tracking performance of leveraged ETFs on
gold, and their price relationships with gold spot and futures. For tracking
the gold spot, we find that our optimized portfolios with short-term gold
futures are highly effective in replicating prices. The market-traded gold ETF
(GLD) also exhibits a similar tracking performance. However, we show that
leveraged gold ETFs tend to underperform their corresponding leveraged
benchmark. Moreover, the underperformance worsens over a longer holding period.
In contrast, we illustrate that a dynamic portfolio of gold futures tracks
significantly better than various static portfolios. The dynamic portfolio also
consistently outperforms the respective market-traded LETFs for different
leverage ratios over multiple years.