pwc-archive/papers-with-abstracts huggingface dataset:
A memory theoretic approach for investigating the roles of language and intuition in mathematical thinking activities
Date: 2019-09-28 00:00:00

Questions concerning origin of mathematical knowledge and roles of language
and intuition (imagery) in mathematical thoughts are long standing and widely
debated. By introspection, mathematicians usually have some beliefs regarding
these questions. But these beliefs are usually in a big contrast with the
recent cognitive theoretic findings concerning mathematics. Contemporary
cognitive science opens new approaches to reformulate the fundamental questions
concerning mathematics and helps mathematicians break through the Platonic
beliefs about the essence and sources of mathematical knowledge. In this
article, we introduce and discuss mathematical thinking activities and
fundamental processes such as symbolic/formal and visual/spatial ones. Two
different aspects of mathematics should be separated in mathematical cognition.
One aspect considers mathematics as an explicit crystallized knowledge. The
other aspect considers mathematics as an ongoing and transient mental
processing. The cognitive processes and corresponding tasks involved in these
aspects are different. Ongoing mathematical activities both elementary and
advanced, demand working memory resources. Using dual-task techniques, we
design some pilot experiments to differentiate the symbolic/formal and
visual/spatial processes. Using this memory theoretic approach, we explain the
crucial roles of language-based processes such as verbal articulation and
instructive speech and also visuo-spatial intuition such as spatial imagery and
mental movement in various aspects of mathematics.
Interpretable Convolutional Neural Networks for Preterm Birth Classification
Date: 2019-09-30 00:00:00
Tasks: Classification, Interpretable Machine Learning

The use of convolutional neural networks (CNNs) for classification tasks has
become dominant in various medical imaging applications. At the same time,
recent advances in interpretable machine learning techniques have shown great
potential in explaining classifiers' decisions. Layer-wise relevance
propagation (LRP) has been introduced as one of these novel methods that aim to
provide visual interpretation for the network's decisions. In this work we
propose the application of 3D CNNs with LRP for the first time for neonatal
T2-weighted magnetic resonance imaging (MRI) data analysis. Through LRP, the
decisions of our trained classifier are transformed into heatmaps indicating
each voxel's relevance for the outcome of the decision. Our resulting LRP
heatmaps reveal anatomically plausible features in distinguishing preterm
neonates from term ones.
Q-learning for POMDP: An application to learning locomotion gaits
Date: 2019-09-30 00:00:00
Tasks: Q-Learning

This paper presents a Q-learning framework for learning optimal locomotion
gaits in robotic systems modeled as coupled rigid bodies. Inspired by
prevalence of periodic gaits in bio-locomotion, an open loop periodic input is
assumed to (say) affect a nominal gait. The learning problem is to learn a new
(modified) gait by using only partial noisy measurements of the state. The
objective of learning is to maximize a given reward modeled as an objective
function in optimal control settings. The proposed control architecture has
three main components: (i) Phase modeling of dynamics by a single phase
variable; (ii) A coupled oscillator feedback particle filter to represent the
posterior distribution of the phase conditioned in the sensory measurements;
and (iii) A Q-learning algorithm to learn the approximate optimal control law.
The architecture is illustrated with the aid of a planar two-body system. The
performance of the learning is demonstrated in a simulation environment.
Super-resolution photoacoustic and ultrasound imaging with sparse arrays
Date: 2019-09-30 00:00:00
Tasks: Super-Resolution

It has previously been demonstrated that model-based reconstruction methods
relying on a priori knowledge of the imaging point spread function (PSF)
coupled to sparsity priors on the object to image can provide super-resolution
in photoacoustic (PA) or in ultrasound (US) imaging. Here, we experimentally
show that such reconstruction also leads to super-resolution in both PA and US
imaging with arrays having much less elements than used conventionally (sparse
arrays). As a proof of concept, we obtained super-resolution PA and US
cross-sectional images of microfluidic channels with only 8 elements of a
128-elements linear array using a reconstruction approach based on a linear
propagation forward model and assuming sparsity of the imaged structure.
Although the microchannels appear indistinguishable in the conventional
delay-and-sum images obtained with all the 128 transducer elements, the applied
sparsity-constrained model-based reconstruction provides super-resolution with
down to only 8 elements. We also report simulation results showing that the
minimal number of transducer elements required to obtain a correct
reconstruction is fundamentally limited by the signal-to-noise ratio. The
proposed method can be straigthforwardly applied to any transducer geometry,
including 2D sparse arrays for 3D super-resolution PA and US imaging.
Physical-Layer Security for Frequency Diverse Array Based Directional Modulation in Fluctuating Two-Ray Fading Channels
Date: 2019-09-29 00:00:00

The frequency diverse array (FDA) based directional modulation (DM)
technology plays an important role in the implementation of the physical-layer
security (PLS) transmission of 5G and beyond communication system. In order to
meet the tremendous increase in mobile data traffic, a new design consuming
less memory for the FDA-DM-based PLS transmission is urgently demanded. In this
paper, an analytical symmetrical multi-carrier FDA model is proposed in three
dimensions, namely, range, azimuth angle, and elevation angle, which differs
from the conventional analytical approach with only range and azimuth angle
considered. Then, a single-point (SP) artificial noise (AN) aided FDA-DM scheme
is proposed, which reduces memory consumption of FDA-DM systems significantly
compared with the conventional zero-forcing (ZF) and singular value
decomposition (SVD) approaches. Moreover, the PLS performance of the proposed
low-memory-consumption FDA-DM scheme is analyzed in fluctuating two-ray (FTR)
fading channels for the first time, including bit error rate (BER), secrecy
rate (SR), and secrecy outage probability (SOP). More importantly, the
closed-form expressions for the lower bound of the average SR and the upper
bound of the SOP are derived, respectively. The effectiveness of the analytical
expressions is verified by numerical simulations. This work opens a way to
lower the memory requirements for the DM-based PLS transmission of 5G and
beyond communication system.
An integrated approach to simulating the vulnerable atherosclerotic plaque
Date: 2019-11-23 00:00:00
Tasks: Descriptive

Analyses of individual atherosclerotic plaques are mostly descriptive,
relying -- for example -- on histological classification by spectral analysis
of ultrasound waves or staining and observing particular cellular components.
Such passive methods have proved useful for characterizing the structure and
vulnerability of plaques but have little quantitative predictive power. In this
viewpoint article, we propose an integrated quantitative framework to
understand the evolution of plaque. The main approach is to use Partial
Differential Equations (PDEs) with macrophages, necrotic cells, oxidized
lipids, oxygen concentration and PDGF as primary variables coupled to a
biomechanical model to describe vessel growth. The model is deterministic,
providing mechanical, morphological, and histological characteristics of an
atherosclerotic vessel at any desired future time point. We discuss the pros
and cons of such a model, how such a model can provide insight to the
clinician, and potentially guide therapy. Finally, we use our model to create
computer-generated animations of a plaque evolution that are in qualitative
agreement with serial ultrasound images published by Kubo et al. (2010) and
hypothesize possible atherogenic mechanisms.
Real-Time Cubature Kalman Filter Parameter Estimation of Blood Pressure Response Characteristics Under Vasoactive Drugs Administration
Date: 2019-09-29 00:00:00
Tasks: parameter estimation

Mathematical modeling and real-time dynamics identification of the mean
arterial blood pressure (MAP) response of a patient to vasoactive drug infusion
can provide a reliable tool for automated drug administration and therefore,
reduce the emergency costs and significantly benefit the patient's MAP
regulation in an intensive care unit. To this end, a dynamic first-order linear
parameter-varying (LPV) model with varying parameters and varying input delay
is considered to capture the MAP response dynamics. Such a model effectively
addresses the complexity and the intra- and inter-patient variability of the
physiological response. We discretize the model and augment the state vector
with model parameters as unknown states of the system and a Bayesian-based
multiple-model square root cubature Kalman filtering (MMSRCKF) approach is
utilized to estimate the model time-varying parameters. Since, unlike the other
model parameters, the input delay cannot be captured by a random-walk process,
a multiple-model module with a posterior probability estimation is implemented
to provide the delay identification. Validation results confirm the
effectiveness of the proposed identification algorithm both in simulation
scenarios and also using animal experiment data.
Stationarity of the detrended price return in stock markets
Authors: Karina Arias-Calluari, Morteza. N. Najafi, Michael S. Harré, Fernando Alonso-Marroquin
Date: 2019-10-02 00:00:00
Tasks: LEMMA, Time Series, Time Series Analysis

This paper proposes a governing equation for stock market indexes that accounts for non-stationary effects. This is a linear Fokker-Planck equation (FPE) that describes the time evolution of the probability distribution function (PDF) of the price return. By applying Ito's lemma, this FPE is associated with a stochastic differential equation (SDE) that models the time evolution of the price return in a fashion different from the classical Black-Scholes equation. Both FPE and SDE equations account for a deterministic part or trend, and a stationary, stochastic part as a q-Gaussian noise. The model is validated using the S\&P500 index's data. After removing the trend from the index, we show that the detrended part is stationary by evaluating the Hurst exponent of the multifractal time series, its power spectrum, and its autocorrelation.
Improved Attention Models for Memory Augmented Neural Network Adaptive Controllers
Date: 2020-03-19 00:00:00
Tasks: Hard Attention

We introduced a {\it working memory} augmented adaptive controller in our
recent work. The controller uses attention to read from and write to the
working memory. Attention allows the controller to read specific information
that is relevant and update its working memory with information based on its
relevance. The retrieved information is used to modify the final control input
computed by the controller. We showed that this modification speeds up
learning. In the above work, we used a soft-attention mechanism for the
adaptive controller. Controllers that use soft attention or hard attention
mechanisms are limited either because they can forget the information or fail
to shift attention when the information they are reading becomes less relevant.
We propose an attention mechanism that comprises of (i) a hard attention
mechanism and additionally (ii) an attention reallocation mechanism. The
attention reallocation enables the controller to reallocate attention to a
different location when the relevance of the location it is reading from
diminishes. The reallocation also ensures that the information stored in the
memory before the shift in attention is retained which can be lost in both soft
and hard attention mechanisms. We illustrate through detailed simulations of
various scenarios for two link robot and three link robot arm systems we
illustrate the effectiveness of the proposed attention mechanism.
Integrating Machine Learning and Multiscale Modeling: Perspectives, Challenges, and Opportunities in the Biological, Biomedical, and Behavioral Sciences
Date: 2019-10-24 00:00:00
Tasks: BIG-bench Machine Learning, Decision Making

Fueled by breakthrough technology developments, the biological, biomedical,
and behavioral sciences are now collecting more data than ever before. There is
a critical need for time- and cost-efficient strategies to analyze and
interpret these data to advance human health. The recent rise of machine
learning as a powerful technique to integrate multimodality, multifidelity
data, and reveal correlations between intertwined phenomena presents a special
opportunity in this regard. However, classical machine learning techniques
often ignore the fundamental laws of physics and result in ill-posed problems
or non-physical solutions. Multiscale modeling is a successful strategy to
integrate multiscale, multiphysics data and uncover mechanisms that explain the
emergence of function. However, multiscale modeling alone often fails to
efficiently combine large data sets from different sources and different levels
of resolution. We show how machine learning and multiscale modeling can
complement each other to create robust predictive models that integrate the
underlying physics to manage ill-posed problems and explore massive design
spaces. We critically review the current literature, highlight applications and
opportunities, address open questions, and discuss potential challenges and
limitations in four overarching topical areas: ordinary differential equations,
partial differential equations, data-driven approaches, and theory-driven
approaches. Towards these goals, we leverage expertise in applied mathematics,
computer science, computational biology, biophysics, biomechanics, engineering
mechanics, experimentation, and medicine. Our multidisciplinary perspective
suggests that integrating machine learning and multiscale modeling can provide
new insights into disease mechanisms, help identify new targets and treatment
strategies, and inform decision making for the benefit of human health.
Spatio-Chromatic Information available from different Neural Layers via Gaussianization
Date: 2020-05-25 00:00:00

How much visual information about the retinal images can be extracted from
the different layers of the visual pathway?. Separate subsystems (e.g. opponent
channels, spatial filters, nonlinearities of the texture sensors) have been
suggested to be organized for optimal information transmission. However, the
efficiency of these different layers has not been measured when they operate
together on colorimetrically calibrated natural images and using multivariate
information-theoretic units over the joint spatio-chromatic array of responses.
  In this work we present a statistical tool to address this question in an
appropriate (multivariate) way. Specifically, we propose an empirical estimate
of the information transmitted by the system based on a recent Gaussianization
technique that reduces the challenging multivariate PDF estimation problem to a
set of simpler univariate estimations. Total correlation measured using the
proposed estimator is consistent with predictions based on the analytical
Jacobian of a standard spatio-chromatic model of the retina-cortex pathway. If
the noise at certain representation is proportional to the dynamic range of the
response, and one assumes sensors of equivalent noise level, transmitted
information shows the following trends: (1) progressively deeper
representations are better in terms of the amount of information about the
input, (2) the transmitted information up to the cortical representation
follows the PDF of natural scenes over the chromatic and achromatic dimensions
of the stimulus space, (3) the contribution of spatial transforms to capture
visual information is substantially bigger than the contribution of chromatic
transforms, and (4) nonlinearities of the responses contribute substantially to
the transmitted information but less than the linear transforms.
Utility-based pricing and hedging of contingent claims in Almgren-Chriss model with temporary price impact
Authors: Ibrahim Ekren, Sergey Nadtochiy
Date: 2019-10-04 00:00:00

In this paper, we construct the utility-based optimal hedging strategy for a European-type option in the Almgren-Chriss model with temporary price impact. The main mathematical challenge of this work stems from the degeneracy of the second order terms and the quadratic growth of the first order terms in the associated HJB equation, which makes it difficult to establish sufficient regularity of the value function needed to construct the optimal strategy in a feedback form. By combining the analytic and probabilistic tools for describing the value function and the optimal strategy, we establish the feedback representation of the latter. We use this representation to derive an explicit asymptotic expansion of the utility indifference price of the option, which allows us to quantify the price impact in options' market via the price impact coefficient in the underlying market.
Efficient Creation of Datasets for Data-Driven Power System Applications
Date: 2020-04-14 00:00:00

Advances in data-driven methods have sparked renewed interest for
applications in power systems. Creating datasets for successful application of
these methods has proven to be very challenging, especially when considering
power system security. This paper proposes a computationally efficient method
to create datasets of secure and insecure operating points. We propose an
infeasibility certificate based on separating hyperplanes that can a-priori
characterize large parts of the input space as insecure, thus significantly
reducing both computation time and problem size. Our method can handle an order
of magnitude more control variables and creates balanced datasets of secure and
insecure operating points, which is essential for data-driven applications.
While we focus on N-1 security and uncertainty, our method can extend to
dynamic security. For PGLib-OPF networks up to 500 buses and up to 125 control
variables, we demonstrate drastic reductions in unclassified input space
volumes and computation time, create balanced datasets, and evaluate an
illustrative data-driven application.
Statistical analysis and stochastic interest rate modelling for valuing the future with implications in climate change mitigation
Date: 2020-02-11 00:00:00
Tasks: Time Series Analysis

High future discounting rates favor inaction on present expending while lower
rates advise for a more immediate political action. A possible approach to this
key issue in global economy is to take historical time series for nominal
interest rates and inflation, and to construct then real interest rates and
finally obtaining the resulting discount rate according to a specific
stochastic model. Extended periods of negative real interest rates, in which
inflation dominates over nominal rates, are commonly observed, occurring in
many epochs and in all countries. This feature leads us to choose a well-known
model in statistical physics, the Ornstein-Uhlenbeck model, as a basic
dynamical tool in which real interest rates randomly fluctuate and can become
negative, even if they tend to revert to a positive mean value. By covering 14
countries over hundreds of years we suggest different scenarios and include an
error analysis in order to consider the impact of statistical uncertainty in
our results. We find that only 4 of the countries have positive long-run
discount rates while the other ten countries have negative rates. Even if one
rejects the countries where hyperinflation has occurred, our results support
the need to consider low discounting rates. The results provided by these
fourteen countries significantly increase the priority of confronting global
actions such as climate change mitigation. We finally extend the analysis by
first allowing for fluctuations of the mean level in the Ornstein-Uhlenbeck
model and secondly by considering modified versions of the Feller and lognormal
models. In both cases, results remain basically unchanged thus demonstrating
the robustness of the results presented.
Dense monocular Simultaneous Localization and Mapping by direct surfel optimization
Date: 2020-02-14 00:00:00
Tasks: Depth Estimation, Monocular Depth Estimation, Simultaneous Localization and Mapping

This work presents a novel approach for monocular dense Simultaneous
Localization and Mapping. The surface to be estimated is represented as a
piecewise planar surface, defined as a group of surfels each having as
parameters its position and normal. These parameters are then directly
estimated from the raw camera pixels measurements, by a Gauss-Newton iterative
process. As far as the authors know, this is the first time this approach is
used for monocular depth estimation. The representation of the surface as a
group of surfels has several advantages. It allows the recovery of robust and
accurate pixel depths, without the need to use a computationally demanding
depth regularization schema. This has the further advantage of avoiding the use
of a physically unlikely surface smoothness prior. New surfels can be correctly
initialized from the information present in nearby surfels, avoiding also the
need to use an expensive initialization routine commonly needed in Gauss-Newton
methods. The method was written in the GLSL shading language, allowing the
usage of GPGPU thus achieving real-time. The method was tested against several
datasets, showing both its depth and normal estimation correctness, and its
scene reconstruction quality. The results presented here showcase the
usefulness of the more physically grounded piecewise planar scene depth prior,
instead of the more commonly pixel depth independence and smoothness prior.
Concepts, Components and Collections of Trading Strategies and Market Color
Authors: Ravi Kashyap
Date: 2019-09-20 00:00:00
Tasks: Asset Management, Management

This paper acts as a collection of various trading strategies and useful pieces of market information that might help to implement such strategies. This list is meant to be comprehensive (though by no means exhaustive) and hence we only provide pointers and give further sources to explore each strategy further. To set the stage for this exploration, we consider the factors that determine good and bad trades, the notions of market efficiency, the real prospect amidst the seemingly high expectations of homogeneous expectations from human beings and the catch-22 connotations that arise while comprehending the true meaning of rational investing. We can broadly classify trading ideas and client market color material into Delta-One and Derivative strategies since this acts as a natural categorization that depends on the expertise of the various trading desks that will implement these strategies. For each strategy, we will have a core idea and we will present different flavors of this central theme to demonstrate that we can easily cater to the varying risk appetites, regional preferences, asset management styles, investment philosophies, liability constraints, investment horizons, notional trading size, trading frequency and other preferences of different market participants.