Counting the learnable functions of structured data

Cover's function counting theorem is a milestone in the theory of artificial neural networks. It provides an answer to the fundamental question of determining how many binary assignments (dichotomies) of $p$ points in $n$ dimensions can be linearly realized. Regrettably, it has proved hard to extend the same approach to more advanced problems than the classification of points. In particular, an emerging necessity is to find methods to deal with structured data, and specifically with non-pointlike patterns. A prominent case is that of invariant recognition, whereby identification of a stimulus is insensitive to irrelevant transformations on the inputs (such as rotations or changes in perspective in an image). An object is therefore represented by an extended perceptual manifold, consisting of inputs that are classified similarly. Here, we develop a function counting theory for structured data of this kind, by extending Cover's combinatorial technique, and we derive analytical expressions for the average number of dichotomies of generically correlated sets of patterns. As an application, we obtain a closed formula for the capacity of a binary classifier trained to distinguish general polytopes of any dimension. These results may help extend our theoretical understanding of generalization, feature extraction, and invariant object recognition by neural networks

Dicke simulators with emergent collective quantum computational abilities

Using an approach inspired from Spin Glasses, we show that the multimode disordered Dicke model is equivalent to a quantum Hopfield network. We propose variational ground states for the system at zero temperature, which we conjecture to be exact in the thermodynamic limit. These ground states contain the information on the disordered qubit-photon couplings. These results lead to two intriguing physical implications. First, once the qubit-photon couplings can be engineered, it should be possible to build scalable pattern-storing systems whose dynamics is governed by quantum laws. Second, we argue with an example how such Dicke quantum simulators might be used as a solver of "hard" combinatorial optimization problems.Comment: 5+2 pages, 2 figures. revisited in the exposition and supplementary added. Comments are welcom

Generalization from correlated sets of patterns in the perceptron

Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns with a given degree of dissimilarity, how easily will a network be able to "unify" their interpretation? This is quantified by the volume of the configurations of synaptic weights that classify the two sets in a similar manner. To show the applicability of our idea in a concrete setting, we compute this quantity for the perceptron, a simple binary classifier, using the classical statistical physics approach in the replica-symmetric ansatz. In this case, we show how an analytical expression measures the "distance-based capacity", the maximum load of patterns sustainable by the network, at fixed dissimilarity between patterns and fixed allowed number of errors. This curve indicates that generalization is possible at any distance, but with decreasing capacity. We propose that a distance-based definition of generalization may be useful in numerical experiments with real-world neural networks, and to explore computationally sub-dominant sets of synaptic solutions

Current quantization and fractal hierarchy in a driven repulsive lattice gas

Driven lattice gases are widely regarded as the paradigm of collective phenomena out of equilibrium. While such models are usually studied with nearest-neighbor interactions, many empirical driven systems are dominated by slowly decaying interactions such as dipole-dipole and Van der Waals forces. Motivated by this gap, we study the non-equilibrium stationary state of a driven lattice gas with slow-decayed repulsive interactions at zero temperature. By numerical and analytical calculations of the particle current as a function of the density and of the driving field, we identify (i) an abrupt breakdown transition between insulating and conducting states, (ii) current quantization into discrete phases where a finite current flows with infinite differential resistivity, and (iii) a fractal hierarchy of excitations, related to the Farey sequences of number theory. We argue that the origin of these effects is the competition between scales, which also causes the counterintuitive phenomenon that crystalline states can melt by increasing the density

Electromagnetic and ultrasonic investigations on a Roman marble slab

The archaeological museum of Rome asked our group about the physical consistency of a marble slab (second to third century AD) that recently fell during its travel as part of an exhibition. We decided to use different methodologies to investigate the slab: namely a pacometer (Protovale Elcometer) to individuate the internal coupling pins, and ground-penetrating radar (GPR) (2000 MHz) and ultrasonic (55 kHz) tomographic high-density surveys to investigate the internal extension of all the visible fractures and to search for the hidden ones. For the ultrasonic data, tests were carried out to optimize the inversion parameters, in particular the cell dimensions. The choice of cell size for the inversion process must take into account the size of the acquisition grid and the ray number acquired. We proposed to calculate a minimum Fresnel’s radius using the sampling frequency instead of that of the probes. For every methodology used, the quality of the acquired data was relatively high. This was then processed and compared to provide information that was useful for some of the insurance problems of the museum. Later on, the data was processed in depth to see how to improve the data processing and interpretation. Finally, the results of this in-depth study were exposed in detail. Ultrasonic and GPR tomographies show a strong correlation, and in particular, the inhomogeneous areas are located in correspondence to the slab injuries

Minimal two-sphere model of the generation of fluid flow at low Reynolds numbers

Locomotion and generation of flow at low Reynolds number are subject to severe limitations due to the irrelevance of inertia: the "scallop theorem" requires that the system have at least two degrees of freedom, which move in non-reciprocal fashion, i.e. breaking time-reversal symmetry. We show here that a minimal model consisting of just two spheres driven by harmonic potentials is capable of generating flow. In this pump system the two degrees of freedom are the mean and relative positions of the two spheres. We have performed and compared analytical predictions, numerical simulation and experiments, showing that a time-reversible drive is sufficient to induce flow.Comment: 5 pages, 3 figures, revised version, corrected typo

Some tests of 3D ultrasonic traveltime tomography on the Eleonora d'Aragona statue (F. Laurana, 1468)

The use of a non-destructive technique in situ can be a valuable diagnostic tool to support verification of restoration, as well as a monitoring technique in works of art or historical monuments. We present a high resolution 3D ultrasonic tomography to one of the most important statues of the Regional Gallery of Palazzo Abatellis of Palermo, the bust of Eleonora d'Aragona by F. Laurana (1430–1502). This technique allowed to study the structural continuity of the material of the marble. Some tests have been carried out to optimize inversion parameters, such as voxel size and to choose between straight and curved rays. We propose to calculate a minimum lateral resolution using the sampling frequency instead of that of the probes. Consequently it was chosen to use a voxel size of 2 cm, lower than the expected resolution, 0.07 m (calculated considering the median ray length), and also to use curved rays instead of straight rays approximation. The resulting model showed velocity values corresponding to a sufficiently homogeneous and well-preserved marble, but in the lower front portion of the trunk at the breasts, that bears the entire weight of the artwork, low velocity values are present

Cytosolic Crowding Drives the Dynamics of Both Genome and Cytosol in Escherichia coli Challenged with Sub-lethal Antibiotic Treatments.

In contrast to their molecular mode of action, the system-level effect of antibiotics on cells is only beginning to be quantified. Molecular crowding is expected to be a relevant global regulator, which we explore here through the dynamic response phenotypes in Escherichia coli, at single-cell resolution, under sub-lethal regimes of different classes of clinically relevant antibiotics, acting at very different levels in the cell. We measure chromosomal mobility through tracking of fast (<15 s timescale) fluctuations of fluorescently tagged chromosomal loci, and we probe the fluidity of the cytoplasm by tracking cytosolic aggregates. Measuring cellular density, we show how the overall levels of macromolecular crowding affect both quantities, regardless of antibiotic-specific effects. The dominant trend is a strong correlation between the effects in different parts of the chromosome and between the chromosome and cytosol, supporting the concept of an overall global role of molecular crowding in cellular physiology.UKRI grant EP/T002778/

Oxidative stress and cardiovascular disease

The endothelium is one of the most important, and certainly the most extensive, organs involved in cardio- vascular homeostasis. The endothelium-derived vasoactive factors inhibiting smooth muscular cells contraction and proliferation, and platelet function, include nitric oxide (NO), prostacyclin and endothelial-derived hyperpolarizing factor. However, endothelial cells can also produce vasoconstrictive, proaggregant, promitogen mediators, such as thromboxane A2, prostaglandin H2, endothelin 1, and angiotensin II. Therefore, any impair- ment of endothelial function may trigger the typical chain of events of atherogenesis, characterised by vasocon- striction, cellular proliferation and thrombosis. In this regard, the biological link between endothelial dysfunction and atherosclerosis is a reduced bioavailability of NO. However, the precise mechanisms by which the endothelial dysfunction occurs remain still unclear. A decreased bioavailability of NO can be caused by its enhanced reactive oxygen species (ROS) breakdown. Oxidative stress may represent a common mechanism by which different cardiovascular risk factors cause endothelial dysfunction and trigger atherothrombotic process

Geophysical study of the hydrothermal reservoir in the Panza area (Ischia, Italy)

The aim of the present work is the reconstruction of the main geometric pattern and the characterisation with geophysical parameters of geological structures lying at small and medium depths in an area of the Ischia island (Italy), where a sensible hydrothermal activity is present