20 research outputs found
Random-Energy Secret Sharing via Extreme Synergy
The random-energy model (REM), a solvable spin-glass model, has impacted an
incredibly diverse set of problems, from protein folding to combinatorial
optimization to many-body localization. Here, we explore a new connection to
secret sharing. We formulate a secret-sharing scheme, based on the REM, and
analyze its information-theoretic properties. Our analyses reveal that the
correlations between subsystems of the REM are highly synergistic and form the
basis for secure secret-sharing schemes. We derive the ranges of temperatures
and secret lengths over which the REM satisfies the requirement of secure
secret sharing. We show further that a special point in the phase diagram
exists at which the REM-based scheme is optimal in its information encoding.
Our analytical results for the thermodynamic limit are in good qualitative
agreement with numerical simulations of finite systems, for which the strict
security requirement is replaced by a tradeoff between secrecy and
recoverability. Our work offers a further example of information theory as a
unifying concept, connecting problems in statistical physics to those in
computation.Comment: 6 pages, 5 figure
Generalized Information Bottleneck for Gaussian Variables
The information bottleneck (IB) method offers an attractive framework for
understanding representation learning, however its applications are often
limited by its computational intractability. Analytical characterization of the
IB method is not only of practical interest, but it can also lead to new
insights into learning phenomena. Here we consider a generalized IB problem, in
which the mutual information in the original IB method is replaced by
correlation measures based on Renyi and Jeffreys divergences. We derive an
exact analytical IB solution for the case of Gaussian correlated variables. Our
analysis reveals a series of structural transitions, similar to those
previously observed in the original IB case. We find further that although
solving the original, Renyi and Jeffreys IB problems yields different
representations in general, the structural transitions occur at the same
critical tradeoff parameters, and the Renyi and Jeffreys IB solutions perform
well under the original IB objective. Our results suggest that formulating the
IB method with alternative correlation measures could offer a strategy for
obtaining an approximate solution to the original IB problem.Comment: 7 pages, 3 figure
Extrinsic vs Intrinsic Criticality in Systems with Many Components
Biological systems with many components often exhibit seemingly critical
behaviors, characterized by atypically large correlated fluctuations. Yet the
underlying causes remain unclear. Here we define and examine two types of
criticality. Intrinsic criticality arises from interactions within the system
which are fine-tuned to a critical point. Extrinsic criticality, in contrast,
emerges without fine tuning when observable degrees of freedom are coupled to
unobserved fluctuating variables. We unify both types of criticality using the
language of learning and information theory. We show that critical
correlations, intrinsic or extrinsic, lead to diverging mutual information
between two halves of the system, and are a feature of learning problems, in
which the unobserved fluctuations are inferred from the observable degrees of
freedom. We argue that extrinsic criticality is equivalent to standard
inference, whereas intrinsic criticality describes fractional learning, in
which the amount to be learned depends on the system size. We show further that
both types of criticality are on the same continuum, connected by a smooth
crossover. In addition, we investigate the observability of Zipf's law, a
power-law rank-frequency distribution often used as an empirical signature of
criticality. We find that Zipf's law is a robust feature of extrinsic
criticality but can be nontrivial to observe for some intrinsically critical
systems, including critical mean-field models. We further demonstrate that
models with global dynamics, such as oscillatory models, can produce observable
Zipf's law without relying on either external fluctuations or fine tuning. Our
findings suggest that while possible in theory, fine tuning is not the only,
nor the most likely, explanation for the apparent ubiquity of criticality in
biological systems with many components.Comment: 13 pages, 9 figure
Energy consumption and cooperation for optimal sensing
The reliable detection of environmental molecules in the presence of noise is
an important cellular function, yet the underlying computational mechanisms are
not well understood. We introduce a model of two interacting sensors which
allows for the principled exploration of signal statistics, cooperation
strategies and the role of energy consumption in optimal sensing, quantified
through the mutual information between the signal and the sensors. Here we
report that in general the optimal sensing strategy depends both on the noise
level and the statistics of the signals. For joint, correlated signals, energy
consuming (nonequilibrium), asymmetric couplings result in maximum information
gain in the low-noise, high-signal-correlation limit. Surprisingly we also find
that energy consumption is not always required for optimal sensing. We
generalise our model to incorporate time integration of the sensor state by a
population of readout molecules, and demonstrate that sensor interaction and
energy consumption remain important for optimal sensing.Comment: 9 pages, 5 figures, Forthcoming in Nature Communication
Exploiting ecology in drug pulse sequences in favour of population reduction
A deterministic population dynamics model involving birth and death for a two-species system, comprising a wild-type and more resistant species competing via logistic growth, is subjected to two distinct stress environments designed to mimic those that would typically be induced by temporal variation in the concentration of a drug (antibiotic or chemotherapeutic) as it permeates through the population and is progressively degraded. Different treatment regimes, involving single or periodical doses, are evaluated in terms of the minimal population size (a measure of the extinction probability), and the population composition (a measure of the selection pressure for resistance or tolerance during the treatment). We show that there exist timescales over which the low-stress regime is as effective as the high-stress regime, due to the competition between the two species. For multiple periodic treatments, competition can ensure that the minimal population size is attained during the first pulse when the high-stress regime is short, which implies that a single short pulse can be more effective than a more protracted regime. Our results suggest that when the duration of the high-stress environment is restricted, a treatment with one or multiple shorter pulses can produce better outcomes than a single long treatment. If ecological competition is to be exploited for treatments, it is crucial to determine these timescales, and estimate for the minimal population threshold that suffices for extinction. These parameters can be quantified by experiment
Repulsive polarons in two-dimensional Fermi gases
We consider a single spin-down impurity atom interacting via an attractive,
short-range potential with a spin-up Fermi sea in two dimensions (2D).
Similarly to 3D, we show how the impurity can form a metastable state (the
"repulsive polaron") with energy greater than that of the non-interacting
impurity. Moreover, we find that the repulsive polaron can acquire a finite
momentum for sufficiently weak attractive interactions. Even though the energy
of the repulsive polaron can become sizeable, we argue that saturated
ferromagnetism is unfavorable in 2D because of the polaron's finite lifetime
and small quasiparticle weight.Comment: 6 pages, 3 figure