Baby-Step Giant-Step Algorithms for the Symmetric Group

We study discrete logarithms in the setting of group actions. Suppose that $G$ is a group that acts on a set $S$. When $r,s \in S$, a solution $g \in G$ to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study the case where $G = S_n$, and develop analogs to the Shanks baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets $A, B \subseteq S_n$ such that every permutation of $S_n$ can be written as a product $ab$ of elements $a \in A$ and $b \in B$. Our deterministic procedure is optimal up to constant factors, in the sense that $A$ and $B$ can be computed in optimal asymptotic complexity, and $|A|$ and $|B|$ are a small constant from $\sqrt{n!}$ in size. We also analyze randomized "collision" algorithms for the same problem

Supply chain forecasting when information is not shared

The operations management literature is abundant in discussions on the benefits of information sharing in supply chains. However, there are many supply chains where information may not be shared due to constraints such as compatibility of information systems, information quality, trust and confidentiality. Furthermore, a steady stream of papers has explored a phenomenon known as Downstream Demand Inference (DDI) where the upstream member in a supply chain can infer the downstream demand without the need for a formal information sharing mechanism. Recent research has shown that, under more realistic circumstances, DDI is not possible with optimal forecasting methods or Single Exponential Smoothing but is possible when supply chains use a Simple Moving Average (SMA) method. In this paper, we evaluate a simple DDI strategy based on SMA for supply chains where information cannot be shared. This strategy allows the upstream member in the supply chain to infer the consumer demand mathematically rather than it being shared. We compare the DDI strategy with the No Information Sharing (NIS) strategy and an optimal Forecast Information Sharing (FIS) strategy in the supply chain. The comparison is made analytically and by experimentation on real sales data from a major European supermarket located in Germany. We show that using the DDI strategy improves on NIS by reducing the Mean Square Error (MSE) of the forecasts, and cutting inventory costs in the supply chain

Feedback from horizontal cells to rod photoreceptors in vertebrate retina.

Retinal horizontal cells (HCs) provide negative feedback to cones, but, largely because annular illumination fails to evoke a depolarizing response in rods, it is widely believed that there is no feedback from HCs to rods. However, feedback from HCs to cones involves small changes in the calcium current (I(Ca)) that do not always generate detectable depolarizing responses. We therefore recorded I(Ca) directly from rods to test whether they were modulated by feedback from HCs. To circumvent problems presented by overlapping receptive fields of HCs and rods, we manipulated the membrane potential of voltage-clamped HCs while simultaneously recording from rods in a salamander retinal slice preparation. Like HC feedback in cones, hyperpolarizing HCs from -14 to -54, -84, and -104 mV increased the amplitude of I(Ca) recorded from synaptically connected rods and caused hyperpolarizing shifts in I(Ca) voltage dependence. These effects were blocked by supplementing the bicarbonate-buffered saline solution with HEPES. In rods lacking light-responsive outer segments, hyperpolarizing neighboring HCs with light caused a negative activation shift and increased the amplitude of I(Ca). These changes in I(Ca) were blocked by HEPES and by inhibiting HC light responses with a glutamate antagonist, indicating that they were caused by HC feedback. These results show that rods, like cones, receive negative feedback from HCs that regulates the amplitude and voltage dependence of I(Ca). HC-to-rod feedback counters light-evoked decreases in synaptic output and thus shapes the transmission of rod responses to downstream visual neurons

The incidence of prostate cancer in Iran: Results of a population-based cancer registry

Background: Little is known about the epidemiology of prostate cancer in Iranian men. We carried out an active prostate cancer surveillance program in five provinces of Iran. Methods: Data used in this study were obtained from population-based cancer registries between 1996 and 2000. Results: The age-standardized incidence rate of prostate carcinoma in the five provinces was 5.1 per 100,000 person-years. No significant difference was seen in the age-standardized incidence rate of prostate cancer within the provinces studied. The mean±SD age of patients with prostate cancer was 67±13.5 years. Conclusion: The incidence of prostate cancer in Iran is very low as compared to the Western countries. This can partly be explained by lack of nationwide screening program, younger age structure and quality of cancer registration system in Iran

Calcium regulates vesicle replenishment at the cone ribbon synapse.

Cones release glutamate-filled vesicles continuously in darkness, and changing illumination modulates this release. Because sustained release in darkness is governed by vesicle replenishment rates, we analyzed how cone membrane potential regulates replenishment. Synaptic release from cones was measured by recording postsynaptic currents in Ambystoma tigrinum horizontal or OFF bipolar cells evoked by depolarization of simultaneously voltage-clamped cones. We measured replenishment after attaining a steady state between vesicle release and replenishment using trains of test pulses. Increasing Ca(2+) currents (I(Ca)) by changing the test step from -30 to -10 mV increased replenishment. Lengthening -30 mV test pulses to match the Ca(2+) influx during 25 ms test pulses to -10 mV produced similar replenishment rates. Reducing Ca(2+) driving force by using test steps to +30 mV slowed replenishment. Using UV flashes to reverse inhibition of I(Ca) by nifedipine accelerated replenishment. Increasing [Ca(2+)](i) by flash photolysis of caged Ca(2+) also accelerated replenishment. Replenishment, but not the initial burst of release, was enhanced by using an intracellular Ca(2+) buffer of 0.5 mm EGTA rather than 5 mm EGTA, and diminished by 1 mm BAPTA. This suggests that although release and replenishment exhibited similar Ca(2+) dependencies, release sites areCa(2+) channels but replenishment sites are \u3e200 nm away. Membrane potential thus regulates replenishment by controlling Ca(2+) influx, principally by effects on replenishment mechanisms but also by altering releasable pool size. This in turn provides a mechanism for converting changes in light intensity into changes in sustained release at the cone ribbon synapse

Implementation of higher-order absorbing boundary conditions for the Einstein equations

We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar gravitational waves in TT gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We demonstrate that the perfectly absorbing boundary condition B_L of order L=l yields no spurious reflections to linear order in perturbation theory. This is in contrast to the lower-order absorbing boundary conditions B_L with L<l, which include the widely used freezing-Psi_0 boundary condition that imposes the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in Class. Quantum Grav

A monomial matrix formalism to describe quantum many-body states

We propose a framework to describe and simulate a class of many-body quantum states. We do so by considering joint eigenspaces of sets of monomial unitary matrices, called here "M-spaces"; a unitary matrix is monomial if precisely one entry per row and column is nonzero. We show that M-spaces encompass various important state families, such as all Pauli stabilizer states and codes, the AKLT model, Kitaev's (abelian and non-abelian) anyon models, group coset states, W states and the locally maximally entanglable states. We furthermore show how basic properties of M-spaces can transparently be understood by manipulating their monomial stabilizer groups. In particular we derive a unified procedure to construct an eigenbasis of any M-space, yielding an explicit formula for each of the eigenstates. We also discuss the computational complexity of M-spaces and show that basic problems, such as estimating local expectation values, are NP-hard. Finally we prove that a large subclass of M-spaces---containing in particular most of the aforementioned examples---can be simulated efficiently classically with a unified method.Comment: 11 pages + appendice

On SAT representations of XOR constraints

We study the representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an "arc-consistent" representation ("AC"), meaning that unit-clause propagation will fix all forced assignments for all possible instantiations of the xor-variables. Our main negative result is that there is no polysize AC-representation in general. On the positive side we show that finding such an AC-representation is fixed-parameter tractable (fpt) in the number of equations. Then we turn to a stronger criterion of representation, namely propagation completeness ("PC") --- while AC only covers the variables of S, now all the variables in F (the variables in S plus auxiliary variables) are considered for PC. We show that the standard translation actually yields a PC representation for one equation, but fails so for two equations (in fact arbitrarily badly). We show that with a more intelligent translation we can also easily compute a translation to PC for two equations. We conjecture that computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing proof of the transformation from AC-representations to monotone circuits, improved wording and literature review; 3rd v. updated literature, strengthened treatment of monotonisation, improved discussions; 4th v. update of literature, discussions and formulations, more details and examples; conference v. to appear LATA 201

Scientific investigations in the Gulf of Mexico and Caribbean Sea during the 1974-1975 Calypso cruise, parts 1 and 2

The distribution and concentrations of the standing crop of phytoplankton and nutrient salts in the Gulf of Mexico and the Caribbean Sea were investigated to provide ground truth for correlating temperature and chlorophyll-a measurements with observations from NASA U-2 aircraft equipped with specially designed sensors for measuring ocean color phenomena. The physical, chemical, and biological data obtained is summarized. Sampling procedures and methods used for determining plant pigments, species composition of phytoplankton, nutrient salt analysis, and the euphotic zones are described

A periodic inventory system of intermittent demand items with fixed lifetimes

Perishable items with a limited lifespan and intermittent/erratic consumption are found in a variety of industrial settings: dealing with such items is challenging for inventory managers. In this study, a periodic inventory control system is analysed, in which items are characterised by intermittent demand and known expiration dates. We propose a new inventory management method, considering both perishability and intermittency constraints. The new method is a modification of a method proposed in the literature, which uses a periodic order-up-to-level inventory policy and a compound Bernoulli demand. We derive the analytical expression of the fill rate and propose a computational procedure to calculate the optimal solution. A comparative numerical analysis is conducted to evaluate the performance of the proposed solution against the standard inventory control method, which does not take into account perishability. The proposed method leads to a bias that is only affected by demand size, in contrast to the standard method which is impacted by more severe biases driven by intermittence and periods before expiration