Instability of frozen-in states in synchronous Hebbian neural networks

The full dynamics of a synchronous recurrent neural network model with Ising binary units and a Hebbian learning rule with a finite self-interaction is studied in order to determine the stability to synaptic and stochastic noise of frozen-in states that appear in the absence of both kinds of noise. Both, the numerical simulation procedure of Eissfeller and Opper and a new alternative procedure that allows to follow the dynamics over larger time scales have been used in this work. It is shown that synaptic noise destabilizes the frozen-in states and yields either retrieval or paramagnetic states for not too large stochastic noise. The indications are that the same results may follow in the absence of synaptic noise, for low stochastic noise.Comment: 14 pages and 4 figures; accepted for publication in J. Phys. A: Math. Ge

Trends in Kemp\u27s Ridley Sea Turtle (Lepidochelys kempii) Relative Abundance, Distribution, and Size Composition in Nearshore Waters of the Northwestern Gulf of Mexico

Long-term monitoring of in-water life history stages of the critically endangered Kemp’s ridley sea turtle (Lepidochelys kempii) is essential for management because it generates information on the species’ at-sea abundance, size composition, distribution, and habitat requirements. We documented trends in Kemp’s ridley size, relative abundance, and distribution using entanglement netting surveys at three study areas adjacent to tidal passes in the northwestern Gulf of Mexico (NWGOM) during intermittent sampling periods from 1991 to 2013. A total of 656 Kemp’s ridley sea turtles were captured ranging in size from 19.5 to 66.3 cm straight carapace length (SCL) (mean = 35.0 cm SCL). The dominance of juveniles (25–40 cm SCL) captured during sampling suggests the nearshore waters of the NWGOM are an important developmental foraging ground for Kemp’s ridley. Characterization of Kemp’s ridley long-term relative abundance reveals a generally stable trend in catch-per-unit-effort (CPUE) across all study areas combined. Based on the increasing trend in the number of hatchlings released from the species’ primary nesting beach, Rancho Nuevo, Mexico, since the early 1990s, the lack of a corresponding overall increase in juvenile abundance at nearshore sampling locations is puzzling. This disparity is most likely an artifact of the present study’s sampling design, but could also indicate shifts in Kemp’s ridley recruitment away from the NWGOM. While conservation efforts have contributed to this species’ overall growth since the 1980s, as measured by the increasing number of nests, recent declines in this rate of increase are a concern and call for a more comprehensive approach to managing Kemp’s ridley recovery efforts

Competitive Exclusion and Limiting Similarity: A Unified Theory

Robustness of coexistence against changes of parameters is investigated in a model-independent manner through analyzing the feed-back loop of population regulation. We define coexistence as fixed point of the community dynamics with no population having zero size. It is demonstrated that the parameter range allowing coexistence shrinks and disappears when the Jacobian of the dynamics decreases to zero. A general notion of regulating factors/variables is introduced. For each population, its 'impact' and 'sensitivity' niches a re defined as the differential impact on, and the differential sensitivity towards, the regulating variables, respectively. Either similarity of the impact niches, or similarity of the sensitivity niches, result in a small Jacobian and in a reduced likelihood of coexistence. For the case of a resource continuum, this result reduces to the usual "limited niches overlap" picture for both kinds of niche. As an extension of these ideas to the coexistence of infinitely many species, we demonstrate that Roughgarden's example for coexistence of a 'continuum' of populations is structurally unstable

Symmetric sequence processing in a recurrent neural network model with a synchronous dynamics

The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the presence of a self-interaction for each unit. Phase diagrams of stationary states are obtained exhibiting phases of retrieval, symmetric and period-two cyclic states as well as correlated and frozen-in states, in the absence of noise. The frozen-in states are destabilised by synaptic noise and well separated regions of correlated and cyclic states are obtained. Excitatory or inhibitory self-interactions yield enlarged phases of fixed-point or cyclic behaviour.Comment: Accepted for publication in Journal of Physics A: Mathematical and Theoretica

Representing Terrain With Mathematical Operators

This work describes a mathematical representation of terrain data consisting of a novel operation, the “drill”. It facilitates the representation of legal terrains, capturing the richness of the physics of the terrain’s generation by digging channels in the surface. Given our current reliance on digital map data, hand-held devices, and GPS navigation systems, the accuracy and compactness of terrain data representations are becoming increasingly important. Representing a terrain as a series of operations that can procedurally regenerate the terrains allows for compact representation that retains more information than height fields, TINs, and other popular representations. Our model relies on the hydrography information extracted from the terrain, and so drainage information is retained during encoding. To determine the shape of the drill along each channel in the channel network, a cross section of the channel is extracted, and a quadratic polynomial is fit to it. We extract the drill representation from a mountainous dataset, using a series of parameters (including size and area of influence of the drill, as well as the density of the hydrography data), and present the accuracy calculated using a series of metrics. We demonstrate that the drill operator provides a viable and accurate terrain representation that captures both the terrain shape and the richness of its generation

Spectra of sparse non-Hermitian random matrices: an analytical solution

We present the exact analytical expression for the spectrum of a sparse non-Hermitian random matrix ensemble, generalizing two classical results in random-matrix theory: this analytical expression forms a non-Hermitian version of the Kesten-Mckay law as well as a sparse realization of Girko's elliptic law. Our exact result opens new perspectives in the study of several physical problems modelled on sparse random graphs. In this context, we show analytically that the convergence rate of a transport process on a very sparse graph depends upon the degree of symmetry of the edges in a non-monotonous way.Comment: 5 pages, 5 figures, 12 pages supplemental materia

Intraperitoneal photodynamic therapy causes a capillary-leak syndrome.

BackgroundIn patients undergoing intraperitoneal (IP) photodynamic therapy (PDT), the combination of aggressive surgical debulking and light therapy causes an apparent systemic capillary-leak syndrome that necessitates significant intensive care unit (ICU) management after surgery.MethodsFrom May 1997 to May 2001, 65 patients underwent surgical debulking and PDT as part of an ongoing phase II trial for disseminated IP cancer. Perioperative data were reviewed retrospectively, and statistical analyses were performed to determine whether any identifiable factors were associated with the need for mechanical ventilation for longer than 1 day and with the occurrence of postoperative complications.ResultsForty-three women and 22 men (mean age, 49 years) were treated. Operative time averaged 9.8 hours, and mean estimated blood loss was 1450 mL. The mean crystalloid requirement for the first 48 hours after surgery was 29.3 L, and 49 patients required blood products. Twenty-four patients were intubated for longer than 24 hours, with a mean of 8.3 days for those intubated longer than 1 day. The median ICU stay was 4 days. Overall, 110 complications developed in 45 (69%) of the 65 patients. Significant complications included 6 patients with acute respiratory distress syndrome, 28 patients with infectious complications, and 4 patients with anastomotic complications. Statistical analyses revealed that surgery-related factors were significantly associated with these complication outcomes.ConclusionsPatients who undergo surgical debulking and IP PDT develop a significant capillary-leak syndrome after surgery that necessitates massive volume resuscitation, careful ICU monitoring, and, frequently, prolonged ventilatory support

Are there approximate relations among transverse momentum dependent distribution functions?

Certain exact relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into approximate ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such ``Wandzura-Wilczek-type approximation'', namely of that connecting h_{1L}^{\perp(1)a}(x) to h_L^a(x), and discuss how it can be further tested by future CLAS and COMPASS data.Comment: 9 pages, 3 figure

Field-dependent heat transport in the Kondo insulator SmB6 : phonons scattered by magnetic impurities

The thermal conductivity $\kappa$ of the Kondo insulator SmB$_6$ was measured at low temperature, down to 70 mK, in magnetic fields up to 15 T, on single crystals grown using both the floating-zone and the flux methods. The residual linear term $\kappa_0/T$ at $T \to 0$ is found to be zero in all samples, for all magnetic fields, in agreement with previous studies. There is therefore no clear evidence of fermionic heat carriers. In contrast to some prior data, we observe a large enhancement of $\kappa(T)$ with increasing field. The effect of field is anisotropic, depending on the relative orientation of field and heat current (parallel or perpendicular), and with respect to the cubic crystal structure. We interpret our data in terms of heat transport predominantly by phonons, which are scattered by magnetic impurities.Comment: publish versio

The phase diagram of L\'evy spin glasses

We study the L\'evy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses becomes transparent in our solution: the local field contains a part propagating along a backbone of strong bonds and a Gaussian noise term due to weak bonds. Our method allows to determine the complete replica symmetric phase diagram, the replica symmetry breaking line and the entropy. The results are compared with simulations and previous calculations using a Gaussian ansatz for the distribution of fields.Comment: 20 pages, 7 figure