5,795 research outputs found
Reduction of Markov Chains using a Value-of-Information-Based Approach
In this paper, we propose an approach to obtain reduced-order models of
Markov chains. Our approach is composed of two information-theoretic processes.
The first is a means of comparing pairs of stationary chains on different state
spaces, which is done via the negative Kullback-Leibler divergence defined on a
model joint space. Model reduction is achieved by solving a
value-of-information criterion with respect to this divergence. Optimizing the
criterion leads to a probabilistic partitioning of the states in the high-order
Markov chain. A single free parameter that emerges through the optimization
process dictates both the partition uncertainty and the number of state groups.
We provide a data-driven means of choosing the `optimal' value of this free
parameter, which sidesteps needing to a priori know the number of state groups
in an arbitrary chain.Comment: Submitted to Entrop
Partitioning Relational Matrices of Similarities or Dissimilarities using the Value of Information
In this paper, we provide an approach to clustering relational matrices whose
entries correspond to either similarities or dissimilarities between objects.
Our approach is based on the value of information, a parameterized,
information-theoretic criterion that measures the change in costs associated
with changes in information. Optimizing the value of information yields a
deterministic annealing style of clustering with many benefits. For instance,
investigators avoid needing to a priori specify the number of clusters, as the
partitions naturally undergo phase changes, during the annealing process,
whereby the number of clusters changes in a data-driven fashion. The
global-best partition can also often be identified.Comment: Submitted to the IEEE International Conference on Acoustics, Speech,
and Signal Processing (ICASSP
An Analysis of the Value of Information when Exploring Stochastic, Discrete Multi-Armed Bandits
In this paper, we propose an information-theoretic exploration strategy for
stochastic, discrete multi-armed bandits that achieves optimal regret. Our
strategy is based on the value of information criterion. This criterion
measures the trade-off between policy information and obtainable rewards. High
amounts of policy information are associated with exploration-dominant searches
of the space and yield high rewards. Low amounts of policy information favor
the exploitation of existing knowledge. Information, in this criterion, is
quantified by a parameter that can be varied during search. We demonstrate that
a simulated-annealing-like update of this parameter, with a sufficiently fast
cooling schedule, leads to an optimal regret that is logarithmic with respect
to the number of episodes.Comment: Entrop
Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry
The exact solution for the energy spectrum of a one-dimensional Hamiltonian
with local two-site interactions and periodic boundary conditions is
determined. The two-site Hamiltonians commute with the symmetry algebra given
by the Drinfeld double D(D_3) of the dihedral group D_3. As such the model
describes local interactions between non-Abelian anyons, with fusion rules
given by the tensor product decompositions of the irreducible representations
of D(D_3). The Bethe ansatz equations which characterise the exact solution are
found through the use of functional relations satisfied by a set of mutually
commuting transfer matrices.Comment: 19 page
The Catalytic and Non-catalytic Functions of the Brahma Chromatin-Remodeling Protein Collaborate to Fine-Tune Circadian Transcription in Drosophila.
Daily rhythms in gene expression play a critical role in the progression of circadian clocks, and are under regulation by transcription factor binding, histone modifications, RNA polymerase II (RNAPII) recruitment and elongation, and post-transcriptional mechanisms. Although previous studies have shown that clock-controlled genes exhibit rhythmic chromatin modifications, less is known about the functions performed by chromatin remodelers in animal clockwork. Here we have identified the Brahma (Brm) complex as a regulator of the Drosophila clock. In Drosophila, CLOCK (CLK) is the master transcriptional activator driving cyclical gene expression by participating in an auto-inhibitory feedback loop that involves stimulating the expression of the main negative regulators, period (per) and timeless (tim). BRM functions catalytically to increase nucleosome density at the promoters of per and tim, creating an overall restrictive chromatin landscape to limit transcriptional output during the active phase of cycling gene expression. In addition, the non-catalytic function of BRM regulates the level and binding of CLK to target promoters and maintains transient RNAPII stalling at the per promoter, likely by recruiting repressive and pausing factors. By disentangling its catalytic versus non-catalytic functions at the promoters of CLK target genes, we uncovered a multi-leveled mechanism in which BRM fine-tunes circadian transcription
The Disestablishment of African American Male Compliant Ambiguity: A Prison Pipeline Essay
There is an apex to each day, a climax, where a decision is made, and a falling action is the result of that decision. Recommendations to combat the never-ending struggle of my invisibility are derived from culturally relevant and culturally responsive frameworks, resiliency frameworks, and ethical caring frameworks. Without systemic reform in local educational settings that includes local teachers, administrators, parents, and students providing new conceptual frameworks for learner and teacher efficacy, the African American male learner will persistently encounter crucial conflicts throughout the School to Prison pipeline while entering a space that has been rendered invisible due to the focus on policy that perpetuates the pipeline. This essay shows that every day when African American boys enter the pipeline, we are faced with two distinct conflicts—Man vs. Man and Man vs. Self—as we navigate an invisible space, compliant ambiguity
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