Storage and retrieval of vector beams of light in a multiple-degree-of-freedom quantum memory

The full structuration of light in the transverse plane, including intensity, phase and polarization, holds the promise of unprecedented capabilities for applications in classical optics as well as in quantum optics and information sciences. Harnessing special topologies can lead to enhanced focusing, data multiplexing or advanced sensing and metrology. Here we experimentally demonstrate the storage of such spatio-polarization-patterned beams into an optical memory. A set of vectorial vortex modes is generated via liquid crystal cell with topological charge in the optic axis distribution, and preservation of the phase and polarization singularities is demonstrated after retrieval, at the single-photon level. The realized multiple-degree-of-freedom memory can find applications in classical data processing but also in quantum network scenarios where structured states have been shown to provide promising attributes, such as rotational invariance

Non-Convex Multi-species Hopfield models

In this work we introduce a multi-species generalization of the Hopfield model for associative memory, where neurons are divided into groups and both inter-groups and intra-groups pair-wise interactions are considered, with different intensities. Thus, this system contains two of the main ingredients of modern Deep neural network architectures: Hebbian interactions to store patterns of information and multiple layers coding different levels of correlations. The model is completely solvable in the low-load regime with a suitable generalization of the Hamilton-Jacobi technique, despite the Hamiltonian can be a non-definite quadratic form of the magnetizations. The family of multi-species Hopfield model includes, as special cases, the 3-layers Restricted Boltzmann Machine (RBM) with Gaussian hidden layer and the Bidirectional Associative Memory (BAM) model.Comment: This is a pre-print of an article published in J. Stat. Phy

A statistical mechanics approach to autopoietic immune networks

The aim of this work is to try to bridge over theoretical immunology and disordered statistical mechanics. Our long term hope is to contribute to the development of a quantitative theoretical immunology from which practical applications may stem. In order to make theoretical immunology appealing to the statistical physicist audience we are going to work out a research article which, from one side, may hopefully act as a benchmark for future improvements and developments, from the other side, it is written in a very pedagogical way both from a theoretical physics viewpoint as well as from the theoretical immunology one. Furthermore, we have chosen to test our model describing a wide range of features of the adaptive immune response in only a paper: this has been necessary in order to emphasize the benefit available when using disordered statistical mechanics as a tool for the investigation. However, as a consequence, each section is not at all exhaustive and would deserve deep investigation: for the sake of completeness, we restricted details in the analysis of each feature with the aim of introducing a self-consistent model.Comment: 22 pages, 14 figur

Machine learning methods for histopathological image analysis

Abundant accumulation of digital histopathological images has led to the increased demand for their analysis, such as computer-aided diagnosis using machine learning techniques. However, digital pathological images and related tasks have some issues to be considered. In this mini-review, we introduce the application of digital pathological image analysis using machine learning algorithms, address some problems specific to such analysis, and propose possible solutions.Comment: 23 pages, 4 figure

Anergy in self-directed B lymphocytes from a statistical mechanics perspective

The ability of the adaptive immune system to discriminate between self and non-self mainly stems from the ontogenic clonal-deletion of lymphocytes expressing strong binding affinity with self-peptides. However, some self-directed lymphocytes may evade selection and still be harmless due to a mechanism called clonal anergy. As for B lymphocytes, two major explanations for anergy developed over three decades: according to "Varela theory", it stems from a proper orchestration of the whole B-repertoire, in such a way that self-reactive clones, due to intensive interactions and feed-back from other clones, display more inertia to mount a response. On the other hand, according to the `two-signal model", which has prevailed nowadays, self-reacting cells are not stimulated by helper lymphocytes and the absence of such signaling yields anergy. The first result we present, achieved through disordered statistical mechanics, shows that helper cells do not prompt the activation and proliferation of a certain sub-group of B cells, which turn out to be just those broadly interacting, hence it merges the two approaches as a whole (in particular, Varela theory is then contained into the two-signal model). As a second result, we outline a minimal topological architecture for the B-world, where highly connected clones are self-directed as a natural consequence of an ontogenetic learning; this provides a mathematical framework to Varela perspective. As a consequence of these two achievements, clonal deletion and clonal anergy can be seen as two inter-playing aspects of the same phenomenon too

The Use of Rhyme, Rhythm, and Melody as a Form of Repetition Priming to Aid in Encoding, Storage, and Retrieval of Semantic Memories in Alzheimer’s Patients

Millions are diagnosed with Alzheimer’s disease annually which can have debilitating effects on patient memory. Thus, finding new ways to help facilitate memory in these patients, especially through non-pharmaceutical means, has become increasingly important. I examined the use of melody, rhyme, and rhythm as encoding mechanisms to aid in the retrieval of long term semantic information by juxtaposing scholarly articles detailing experiments, each of which examined the effects of various facets of memory facilitation; this helped produce an idea of which devices are most effective. Additionally, I surveyed studies highlighting limitations of song implementation to craft an effective plan to aid Alzheimer’s patients. Melody, rhyme, and rhythm provide an organizational structure to facilitate the encoding of information. Specifically, chunking, the grouping of smaller units into larger ‘chunks’, helps facilitate long term encoding in patients, and is the byproduct of the organizational structure of a text. A major drawback of using these devices is the loss in the depth of encoding semantic information; however, it is important to recognize music still assists general content memory. Therefore, Alzheimer’s patients would benefit from the use of melody as it would provide a moral support, helping familiarity with their surroundings, although they would not benefit from instructional song. Future experiments may study the combination of discussed factors in various settings to examine the unique benefits of music on memory in Alzheimer’s patients

Free energies of Boltzmann Machines: self-averaging, annealed and replica symmetric approximations in the thermodynamic limit

Restricted Boltzmann machines (RBMs) constitute one of the main models for machine statistical inference and they are widely employed in Artificial Intelligence as powerful tools for (deep) learning. However, in contrast with countless remarkable practical successes, their mathematical formalization has been largely elusive: from a statistical-mechanics perspective these systems display the same (random) Gibbs measure of bi-partite spin-glasses, whose rigorous treatment is notoriously difficult. In this work, beyond providing a brief review on RBMs from both the learning and the retrieval perspectives, we aim to contribute to their analytical investigation, by considering two distinct realizations of their weights (i.e., Boolean and Gaussian) and studying the properties of their related free energies. More precisely, focusing on a RBM characterized by digital couplings, we first extend the Pastur-Shcherbina-Tirozzi method (originally developed for the Hopfield model) to prove the self-averaging property for the free energy, over its quenched expectation, in the infinite volume limit, then we explicitly calculate its simplest approximation, namely its annealed bound. Next, focusing on a RBM characterized by analogical weights, we extend Guerra's interpolating scheme to obtain a control of the quenched free-energy under the assumption of replica symmetry: we get self-consistencies for the order parameters (in full agreement with the existing Literature) as well as the critical line for ergodicity breaking that turns out to be the same obtained in AGS theory. As we discuss, this analogy stems from the slow-noise universality. Finally, glancing beyond replica symmetry, we analyze the fluctuations of the overlaps for an estimate of the (slow) noise affecting the retrieval of the signal, and by a stability analysis we recover the Aizenman-Contucci identities typical of glassy systems.Comment: 21 pages, 1 figur