pwc-archive/papers-with-abstracts huggingface dataset:
Theoretical Levels of Control as a Function of Mean Temperature and Spray Efficacy in the Aerial Spraying of Tsetse Fly
Date: 2015-10-28 00:00:00

The hypothetical impact of aerial spraying on tsetse fly populations is
investigated. Spray cycles are scheduled at intervals two days short of the
first interlarval period and halted once the last of the female flies that
originated from pre-spray-deposited pupae have been sprayed twice. The effect
of temperature on the aerial spraying of tsetse, through its reproductive cycle
and general population dynamics, is of particular interest, given that cooler
weather is preferred for the settling of insecticidal droplets. Spray efficacy
is found to come at a price due to the greater number of cycles necessitated by
cooler weather. The extra cost is argued to be worth while. Pupae, still in the
ground at the end of spraying, are identified as the main threat to a
successful operation. They are slightly more vulnerable at the low temperature
extreme of tsetse habitat (16 $^\circ$C), when the cumulative, natural pupal
mortality is high. One can otherwise base one's expectations on the closeness
with which the time to the third last spray approaches one puparial duration. A
disparity of anything close to the length of a spray cycle advocates caution,
whereas one which comes close to vanishing should be interpreted as being
auspicious. Three such key temperatures, just below which one can anticipate an
improved outcome and just above which caution should be exercised, are 17.146
$^\circ$C, 19.278 $^\circ$C and 23.645 $^\circ$C. A refinement of the existing
formulae for the puparial duration and the first interlarval period might be
prudent in the South African context of a sympatric Glossina brevipalpis-G.
austeni, tsetse population. The resulting aerial spraying strategy would then
be formulated using a G. brevipalpis puparial duration and a G. austeni first
interlarval period.
The URDME manual Version 1.4
Date: 2020-01-27 00:00:00

We have developed URDME, a general software for simulation of stochastic
reaction-diffusion processes on unstructured meshes. This allows for a more
flexible handling of complicated geometries and curved boundaries compared to
simulations on structured, cartesian meshes. The underlying algorithm is the
next subvolume method, extended to unstructured meshes by obtaining jump
coefficients from a finite element formulation of the corresponding macroscopic
equation.
  This manual describes version 1.4 of the software. Refer to www.urdme.org for
the latest updates.
Quantum calcium-ion interactions with EEG
Date: 2019-11-23 00:00:00
Tasks: EEG, Electroencephalogram (EEG)

Previous papers have developed a statistical mechanics of neocortical
interactions (SMNI) fit to short-term memory and EEG data. Adaptive Simulated
Annealing (ASA) has been developed to perform fits to such nonlinear stochastic
systems. An N-dimensional path-integral algorithm for quantum systems,
qPATHINT, has been developed from classical PATHINT. Both fold short-time
propagators (distributions or wave functions) over long times. Previous papers
applied qPATHINT to two systems, in neocortical interactions and financial
options. \textbf{Objective}: In this paper the quantum path-integral for
Calcium ions is used to derive a closed-form analytic solution at arbitrary
time that is used to calculate interactions with classical-physics SMNI
interactions among scales. Using fits of this SMNI model to EEG data, including
these effects, will help determine if this is a reasonable approach.
\textbf{Method}: Methods of mathematical-physics for optimization and for path
integrals in classical and quantum spaces are used for this project. Studies
using supercomputer resources tested various dimensions for their scaling
limits. In this paper the quantum path-integral is used to derive a closed-form
analytic solution at arbitrary time that is used to calculate interactions with
classical-physics SMNI interactions among scales. \textbf{Results}: The
mathematical-physics and computer parts of the study are successful, in that
there is modest improvement of cost/objective functions used to fit EEG data
using these models. \textbf{Conclusion}: This project points to directions for
more detailed calculations using more EEG data and qPATHINT at each time slice
to propagate quantum calcium waves, synchronized with PATHINT propagation of
classical SMNI.
Asymptotic Implied Volatility at the Second Order with Application to the SABR Model
Date: 2016-05-17 00:00:00

We provide a general method to compute a Taylor expansion in time of implied
volatility for stochastic volatility models, using a heat kernel expansion.
Beyond the order 0 implied volatility which is already known, we compute the
first order correction exactly at all strikes from the scalar coefficient of
the heat kernel expansion. Furthermore, the first correction in the heat kernel
expansion gives the second order correction for implied volatility, which we
also give exactly at all strikes. As an application, we compute this asymptotic
expansion at order 2 for the SABR model.
Law of the Minimum Paradoxes
Date: 2019-11-12 00:00:00
Tasks: Econometrics

The "Law of the Minimum" states that growth is controlled by the scarcest
resource (limiting factor). This concept was originally applied to plant or
crop growth (Justus von Liebig, 1840) and quantitatively supported by many
experiments. Some generalizations based on more complicated "dose-response"
curves were proposed. Violations of this law in natural and experimental
ecosystems were also reported. We study models of adaptation in ensembles of
similar organisms under load of environmental factors and prove that violation
of Liebig's law follows from adaptation effects. If the fitness of an organism
in a fixed environment satisfies the Law of the Minimum then adaptation
equalizes the pressure of essential factors and therefore acts against the
Liebig's law. This is the the Law of the Minimum paradox: if for a randomly
chosen pair "organism-environment" the Law of the Minimum typically holds,
then, in a well-adapted system, we have to expect violations of this law.
  For the opposite interaction of factors (a synergistic system of factors
which amplify each other) adaptation leads from factor equivalence to
limitations by a smaller number of factors.
  For analysis of adaptation we develop a system of models based on Selye's
idea of the universal adaptation resource (adaptation energy). These models
predict that under the load of an environmental factor a population separates
into two groups (phases): a less correlated, well adapted group and a highly
correlated group with a larger variance of attributes, which experiences
problems with adaptation. Some empirical data are presented and evidences of
interdisciplinary applications to econometrics are discussed.
Geometric Arbitrage Theory and Market Dynamics Reloaded
Authors: Simone Farinelli
Date: 2009-10-09 00:00:00

We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature of a principal fibre bundle. --Parameterize arbitrage strategies by its holonomy. --Give the Fundamental Theorem of Asset Pricing a differential homotopic characterization. --Characterize Geometric Arbitrage Theory by five principles and show they they are consistent with the classical theory of stochastic finance. --Derive for a closed market the equilibrium solution for market portfolio and dynamics in the cases where: -->Arbitrage is allowed but minimized. -->Arbitrage is not allowed. --Prove that the no-free-lunch-with-vanishing-risk condition implies the zero curvature condition.
The Finite Element Implementation of a K.P.P. Equation for the Simulation of Tsetse Control Measures in the Vicinity of a Game Reserve
Date: 2015-05-25 00:00:00

An equation, strongly reminiscent of Fisher's equation, is used to model the
response of tsetse populations to proposed control measures in the vicinity of
a game reserve. The model assumes movement is by diffusion and that growth is
logistic. This logistic growth is dependent on an historical population, in
contrast to Fisher's equation which bases it on the present population. The
model therefore takes into account the fact that new additions to the adult fly
population are, in actual fact, the descendents of a population which existed
one puparial duration ago, furthermore, that this puparial duration is
temperature dependent. Artificially imposed mortality is modelled as a
proportion at a constant rate. Fisher's equation is also solved as a formality.
  The temporary imposition of a 2 % $\mathrm{day}^{-1}$ mortality everywhere
outside the reserve for a period of 2 years will have no lasting effect on the
influence of the reserve on either the Glossina austeni or the G. brevipalpis
populations, although it certainly will eradicate tsetse from poor habitat,
outside the reserve. A 5 $\mathrm{km}$-wide barrier with a minimum mortality of
4 % $\mathrm{day}^{-1}$, throughout, will succeed in isolating a worst-case, G.
austeni population and its associated trypanosomiasis from the surrounding
areas. A more optimistic estimate of its mobility suggests a mortality of 2 %
$\mathrm{day}^{-1}$ will suffice. For a given target-related mortality, more
mobile species are found to be more vulnerable to eradication than more
sedentary species, while the opposite is true for containment.
A remark on Gatheral's 'most-likely path approximation' of implied volatility
Date: 2016-10-13 00:00:00

We give a new proof of the representation of implied volatility as a
time-average of weighted expectations of local or stochastic volatility. With
this proof we clarify the question of existence of 'forward implied variance'
in the original derivation of Gatheral, who introduced this representation in
his book 'The Volatility Surface'.
Modularity map of the network of human cell differentiation
Date: 2016-03-28 00:00:00

Cell differentiation in multicellular organisms is a complex process whose
mechanism can be understood by a reductionist approach, in which the individual
processes that control the generation of different cell types are identified.
Alternatively, a large scale approach in search of different organizational
features of the growth stages promises to reveal its modular global structure
with the goal of discovering previously unknown relations between cell types.
Here we sort and analyze a large set of scattered data to construct the network
of human cell differentiation (NHCD) based on cell types (nodes) and
differentiation steps (links) from the fertilized egg to a crying baby. We
discover a dynamical law of critical branching, which reveals a fractal
regularity in the modular organization of the network, and allows us to observe
the network at different scales. The emerging picture clearly identifies
clusters of cell types following a hierarchical organization, ranging from
sub-modules to super-modules of specialized tissues and organs on varying
scales. This discovery will allow one to treat the development of a particular
cell function in the context of the complex network of human development as a
whole. Our results point to an integrated large-scale view of the network of
cell types systematically revealing ties between previously unrelated domains
in organ functions.
The two defaults scenario for stressing credit portfolio loss distributions
Date: 2015-10-25 00:00:00
Tasks: Vocal Bursts Valence Prediction

The impact of a stress scenario of default events on the loss distribution of
a credit portfolio can be assessed by determining the loss distribution
conditional on these events. While it is conceptually easy to estimate loss
distributions conditional on default events by means of Monte Carlo simulation,
it becomes impractical for two or more simultaneous defaults as then the
conditioning event is extremely rare. We provide an analytical approach to the
calculation of the conditional loss distribution for the CreditRisk+ portfolio
model with independent random loss given default distributions. The analytical
solution for this case can be used to check the accuracy of an approximation to
the conditional loss distribution whereby the unconditional model is run with
stressed input probabilities of default (PDs). It turns out that this
approximation is unbiased. Numerical examples, however, suggest that the
approximation may be seriously inaccurate but that the inaccuracy leads to
overestimation of tail losses and hence the approach errs on the conservative
side.
Average sex ratio and population maintenance cost
Date: 2017-02-14 00:00:00

The ratio of males to females in a population is a meaningful characteristic
of sexual species. The reason for this biological property to be available to
the observers of nature seems to be a question never asked. Introducing the
notion of historically adapted populations as global minimizers of maintenance
cost functions, we propose a theoretical explanation for the reported stability
of this feature. This mathematical formulation suggests that sex ratio could be
considered as an indirect result shaped by the antagonism between the size of
the population and the finiteness of resources.
Rough paths in idealized financial markets
Date: 2016-11-28 00:00:00

This paper considers possible price paths of a financial security in an
idealized market. Its main result is that the variation index of typical price
paths is at most 2, in this sense, typical price paths are not rougher than
typical paths of Brownian motion. We do not make any stochastic assumptions and
only assume that the price path is positive and right-continuous. The
qualification "typical" means that there is a trading strategy (constructed
explicitly in the proof) that risks only one monetary unit but brings infinite
capital when the variation index of the realized price path exceeds 2. The
paper also reviews some known results for continuous price paths and lists
several open problems.
Certifiably Pseudorandom Financial Derivatives
Date: 2019-08-31 00:00:00

Arora, Barak, Brunnermeier, and Ge showed that taking computational
complexity into account, a dishonest seller could strategically place lemons in
financial derivatives to make them substantially less valuable to buyers. We
show that if the seller is required to construct derivatives of a certain form,
then this phenomenon disappears. In particular, we define and construct
pseudorandom derivative families, for which lemon placement only slightly
affects the values of the derivatives. Our constructions use expander graphs.
We study our derivatives in a more general setting than Arora et al. In
particular, we analyze arbitrary tranches of the common collateralized debt
obligations (CDOs) when the underlying assets can have significant
dependencies.
Role of Antibodies: A Novel Paradigm in Mathematical Modeling for Cancer Treatment
Date: 2016-10-18 00:00:00

A mathematical model for the quantitative analysis of cancer immune
interaction, considering the role of antibodies has been proposed in this
paper. The model is based on the clinical evidence, which states that
antibodies can directly kill cancerous cells [1]. The existence of
transcritical and saddle-node bifurcation, which has been proved using
Sotomayor theorem, provides strong biological implications. Through numerical
simulations, it has been illustrated that under certain therapy (like
monoclonal antibody therapy), which is capable of altering the parameters of
the system, cancer-free state can be obtained.
Quantitative Analysis by the Point-Centered Quarter Method
Authors: Kevin Mitchell
Date: 2010-10-16 00:00:00

This document is an introduction to the use of the point-centered quarter method. It briefly outlines its history, its methodology, and some of the practical issues (and modifications) that inevitably arise with its use in the field. Additionally this paper shows how data collected using point-centered quarter method sampling may be used to determine importance values of different species of trees and describes and derives several methods of estimating plant density and corresponding confidence intervals. New to this version is a revision of Appendix D which now includes R Shiny Apps to carry out many of these calculations. References to data sets in the previous version that are no longer publicly available have been removed. These have been replaced with examples and exercises which demonstrate the use of the R Shiny Apps and the earlier R scripts.
Risk-Neutral Pricing of Financial Instruments in Emission Markets: A Structural Approach
Date: 2015-05-29 00:00:00

We present a novel approach to the pricing of financial instruments in
emission markets, for example, the EU ETS. The proposed structural model is
positioned between existing complex full equilibrium models and pure reduced
form models. Using an exogenously specified demand for a polluting good it
gives a causal explanation for the accumulation of CO2 emissions and takes into
account the feedback effect from the cost of carbon to the rate at which the
market emits CO2. We derive a forward-backward stochastic differential equation
for the price process of the allowance certificate and solve the associated
semilinear partial differential equation numerically. We also show that
derivatives written on the allowance certificate satisfy a linear partial
differential equation. The model is extended to emission markets with multiple
compliance periods and we analyse the impact different intertemporal connecting
mechanisms, such as borrowing, banking and withdrawal, have on the allowance
price.
Cluster-scaling, chaotic order and coherence in DNA
Date: 2018-01-29 00:00:00

Different numerical mappings of the DNA sequences have been studied using a
new cluster-scaling method and the well known spectral methods. It is shown, in
particular, that the nucleotide sequences in DNA molecules have robust
cluster-scaling properties. These properties are relevant to both types of
nucleotide pair-bases interactions: hydrogen bonds and stacking interactions.
It is shown that taking into account the cluster-scaling properties can help to
improve heterogeneous models of the DNA dynamics. It is also shown that a
chaotic (deterministic) order, rather than a stochastic randomness, controls
the energy minima positions of the stacking interactions in the DNA sequences
on large scales. The chaotic order results in a large-scale chaotic coherence
between the two complimentary DNA-duplex's sequences. A competition between
this broad-band chaotic coherence and the resonance coherence produced by
genetic code has been briefly discussed. The Arabidopsis plant genome (which is
a model plant for genome analysis) and two human genes: BRCA2 and NRXN1, have
been considered as examples.
The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts
Date: 2016-04-12 00:00:00
Tasks: Diversity

Matrix forms of the representation of the multi-level system of
molecular-genetic alphabets have revealed algebraic properties of this system.
Families of genetic (4*4)- and (8*8)-matrices show unexpected connections of
the genetic system with Walsh functions and Hadamard matrices, which are known
in theory of noise-immunity coding, digital communication and digital
holography. Dyadic-shift decompositions of such genetic matrices lead to sets
of sparse matrices. Each of these sets is closed in relation to multiplication
and defines relevant algebra of hypercomplex numbers. It is shown that genetic
Hadamard matrices are identical to matrix representations of Hamilton
quaternions and its complexification in the case of unit coordinates. The
diversity of known dialects of the genetic code is analyzed from the viewpoint
of the genetic algebras. An algebraic analogy with Punnett squares for
inherited traits is shown. Our results are used in analyzing genetic phenomena.
The statement about existence of the geno-logic code in DNA and epigenetics on
the base of the spectral logic of systems of Boolean functions is put forward.
Our results show promising ways to develop algebraic-logical biology, in
particular, in connection with the logic holography on Walsh functions.
Theoretical Sensitivity Analysis for Quantitative Operational Risk Management
Date: 2017-05-24 00:00:00
Tasks: Management, Sensitivity

We study the asymptotic behavior of the difference between the values at risk
VaR(L) and VaR(L+S) for heavy tailed random variables L and S for application
in sensitivity analysis of quantitative operational risk management within the
framework of the advanced measurement approach of Basel II (and III). Here L
describes the loss amount of the present risk profile and S describes the loss
amount caused by an additional loss factor. We obtain different types of
results according to the relative magnitudes of the thicknesses of the tails of
L and S. In particular, if the tail of S is sufficiently thinner than the tail
of L, then the difference between prior and posterior risk amounts VaR(L+S) -
VaR(L) is asymptotically equivalent to the expectation (expected loss) of S.
What does photon energy tell us about cellphone safety?
Date: 2017-04-25 00:00:00

It has been argued that cellphones are safe because a single microwave photon
does not have enough energy to break a chemical bond. We show that cellphone
technology operates in the classical wave limit, not the single photon limit.
Based on energy densities relative to thermal energy, we estimate thresholds at
which effects might be expected. These seem to correspond somewhat with many
experimental observations.
  Revised with appendix responding to critique published by B. Leikind.
Exponential utility with non-negative consumption
Date: 2019-06-25 00:00:00

We offer mathematical tractability and new insights for a framework of
exponential utility with non-negative consumption, a constraint often omitted
in the literature giving rise to economically unviable solutions. Specifically,
using the Kuhn-Tucker theorem and the notion of aggregate state price density
(Malamud and Trubowitz (2007)), we provide a solution to this problem in the
setting of both complete and incomplete markets (with random endowments). Then,
we exploit this result to provide an explicit characterization of complete
market heterogeneous equilibria. Furthermore, we construct concrete examples of
models admitting multiple (including infinitely many) equilibria. By using
Cramer's large deviation theorem, we study the asymptotics of equilibrium zero
coupon bonds. Lastly, we conduct a study of the precautionary savings motive in
incomplete markets.
When can dictionary learning uniquely recover sparse data from subsamples?
Date: 2015-07-31 00:00:00
Tasks: Dictionary Learning, LEMMA

Sparse coding or sparse dictionary learning has been widely used to recover
underlying structure in many kinds of natural data. Here, we provide conditions
guaranteeing when this recovery is universal; that is, when sparse codes and
dictionaries are unique (up to natural symmetries). Our main tool is a useful
lemma in combinatorial matrix theory that allows us to derive bounds on the
sample sizes guaranteeing such uniqueness under various assumptions for how
training data are generated. Whenever the conditions to one of our theorems are
met, any sparsity-constrained learning algorithm that succeeds in
reconstructing the data recovers the original sparse codes and dictionary. We
also discuss potential applications to neuroscience and data analysis.