Tight Bounds for the Randomized and Quantum Communication Complexities of Equality with Small Error

We investigate the randomized and quantum communication complexities of the well-studied Equality function with small error probability $\epsilon$, getting the optimal constant factors in the leading terms in a number of different models. In the randomized model, 1) we give a general technique to convert public-coin protocols to private-coin protocols by incurring a small multiplicative error, at a small additive cost. This is an improvement over Newman's theorem [Inf. Proc. Let.'91] in the dependence on the error parameter. 2) Using this we obtain a $(\log(n/\epsilon^2)+4)$-cost private-coin communication protocol that computes the $n$-bit Equality function, to error $\epsilon$. This improves upon the $\log(n/\epsilon^3)+O(1)$ upper bound implied by Newman's theorem, and matches the best known lower bound, which follows from Alon [Comb. Prob. Comput.'09], up to an additive $\log\log(1/\epsilon)+O(1)$. In the quantum model, 1) we exhibit a one-way protocol of cost $\log(n/\epsilon)+4$, that uses only pure states and computes the $n$-bit Equality function to error $\epsilon$. This bound was implicitly already shown by Nayak [PhD thesis'99]. 2) We show that any $\epsilon$-error one-way protocol for $n$-bit Equality that uses only pure states communicates at least $\log(n/\epsilon)-\log\log(1/\epsilon)-O(1)$ qubits. 3) We exhibit a one-way protocol of cost $\log(\sqrt{n}/\epsilon)+3$, that uses mixed states and computes the $n$-bit Equality function to error $\epsilon$. This is also tight up to an additive $\log\log(1/\epsilon)+O(1)$, which follows from Alon's result. Our upper bounds also yield upper bounds on the approximate rank and related measures of the Identity matrix. This also implies improved upper bounds on these measures for the distributed SINK function, which was recently used to refute the randomized and quantum versions of the log-rank conjecture.Comment: 16 page

Proterozoic ocean redox and biogeochemical stasis

The partial pressure of oxygen in Earth’s atmosphere has increased dramatically through time, and this increase is thought to have occurred in two rapid steps at both ends of the Proterozoic Eon (∼2.5–0.543 Ga). However, the trajectory and mechanisms of Earth’s oxygenation are still poorly constrained, and little is known regarding attendant changes in ocean ventilation and seafloor redox. We have a particularly poor understanding of ocean chemistry during the mid-Proterozoic (∼1.8–0.8 Ga). Given the coupling between redox-sensitive trace element cycles and planktonic productivity, various models for mid-Proterozoic ocean chemistry imply different effects on the biogeochemical cycling of major and trace nutrients, with potential ecological constraints on emerging eukaryotic life. Here, we exploit the differing redox behavior of molybdenum and chromium to provide constraints on seafloor redox evolution by coupling a large database of sedimentary metal enrichments to a mass balance model that includes spatially variant metal burial rates. We find that the metal enrichment record implies a Proterozoic deep ocean characterized by pervasive anoxia relative to the Phanerozoic (at least ∼30–40% of modern seafloor area) but a relatively small extent of euxinic (anoxic and sulfidic) seafloor (less than ∼1–10% of modern seafloor area). Our model suggests that the oceanic Mo reservoir is extremely sensitive to perturbations in the extent of sulfidic seafloor and that the record of Mo and chromium enrichments through time is consistent with the possibility of a Mo–N colimited marine biosphere during many periods of Earth’s history

The effects of immigration on wages: An application of the structural skill-cell approach

This paper investigates how recent immigration inflows from 2002 to 2008 have affected wages in Switzerland. This period is of particular interest as it marks the time during which the bilateral agreement with the EU on the free cross-border movement of workers has been effective. Since different types of workers are likely to be unevenly affected by recent immigration inflows, we follow the ”structural skill-cell approach” as for example employed by Borjas (2003) and Ottaviano and Peri (2008). This paper provides two main contributions. First, we estimate empirically the elasticities of substitution between different types of workers in Switzerland. Our results suggest that natives and immigrants are imperfect substitutes. Regarding different skill levels, the estimates indicate that workers are imperfect substitutes across broad education groups and across different experience groups. Second, the estimated elasticities of substitution are used to simulate the impact on domestic wages using the actual immigration inflows from 2002 to 2008. For the long run, the simulations produce some notable distributional consequences across different types of workers: While previous immigrants incur wage losses (−1.6%), native workers are not negatively affected on average (+0.4%). In the short run, immigration has a negative macroeconomic effect on the average wage, which, however, gradually dies out in the process of capital adjustment

Authigenic iron oxide proxies for marine zinc over geological time and implications for eukaryotic metallome evolution

Author Posting. © The Author(s), 2012. This is the author's version of the work. It is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Geobiology 11 (2013): 295-306, doi:10.1111/gbi.12036.Here we explore enrichments in paleomarine Zn as recorded by authigenic iron oxides including Precambrian iron formations, ironstones and Phanerozoic hydrothermal exhalites. This compilation of new and literature-based iron formation analyses track dissolved Zn abundances and constrain the magnitude of the marine reservoir over geological time. Overall, the iron formation record is characterized by a fairly static range in Zn/Fe ratios throughout the Precambrian, consistent with the shale record (Scott et al., 2013, Nature Geoscience, 6, 125-128). When hypothetical partitioning scenarios are applied to this record, paleomarine Zn concentrations within about an order of magnitude of modern are indicated. We couple this examination with new chemical speciation models used to interpret the iron formation record. We present two scenarios: first, under all but the most sulfidic conditions and with Zn binding organic ligand concentrations similar to modern oceans, the amount of bioavailable Zn remained relatively unchanged through time. Late proliferation of Zn in eukaryotic metallomes has previously been linked to marine Zn biolimitation, but under this scenario, the expansion in eukaryotic Zn metallomes may be better linked to biologically intrinsic evolutionary factors. In this case zinc’s geochemical and biological evolution may be decoupled, and viewed as a function of increasing need for genome regulation and diversification of Zn-binding transcription factors. In the second scenario, we consider Archean organic ligand complexation in such excess that it may render Zn bioavailability low. However, this is dependent on Zn organic ligand complexes not being bioavailable, which remains unclear. In this case, although bioavailability may be low, sphalerite precipitation is prevented, thereby maintaining a constant Zn inventory throughout both ferruginous and euxinic conditions. These results provide new perspectives and constraints 50 on potential couplings between the trajectory of biological and marine geochemical coevolution.This work was supported by a NSERC Discovery Grant to KOK, a NSERC PDF to SVL, a NSERC CGSM to LJR, and an NSF-EAR-PDF to NJP. MAS acknowledges support from the Gordon and Betty Moore Foundation Grant #2724. This work was also supported by grants from the Deutsche Forschungsgemeinschaft (DFG) to A.K. (KA 1736/4-1 and 12-1)

Animal tissue-based quantitative comparison of dual-energy CT to SPR conversion methods using high-resolution gel dosimetry

Dual-energy computed tomography (DECT) has been shown to allow for more accurate ion therapy treatment planning by improving the estimation of tissue stopping power ratio (SPR) relative to water, among other tissue properties. In this study, we measured and compared the accuracy of SPR values derived using both dual- and single-energy CT (SECT) based on different published conversion algorithms. For this purpose, a phantom setup containing either fresh animal soft tissue samples (beef, pork) and a water reference or tissue equivalent plastic materials was designed and irradiated in a clinical proton therapy facility. Dosimetric polymer gel was positioned downstream of the samples to obtain a three-dimensional proton range distribution with high spatial resolution. The mean proton range in gel for each tissue relative to the water sample was converted to a SPR value. Additionally, the homogeneous samples were probed with a variable water column encompassed by two ionization chambers to benchmark the SPR accuracy of the gel dosimetry. The SPR values measured with both methods were consistent with a mean deviation of 0.2%, but the gel dosimetry captured range variations up to 5 mm within individual samples. Across all fresh tissue samples the SECT approach yielded significantly greater mean absolute deviations from the SPR deduced using gel range measurements, with an average difference of 1.2%, compared to just 0.3% for the most accurate DECT-based algorithm. These results show a significant advantage of DECT over SECT for stopping power prediction in a realistic setting, and for the first time allow to compare a large set of methods under the same conditions

Neural changes associated with appetite information processing in schizophrenic patients after 16 weeks of olanzapine treatment

There is evidence that some atypical antipsychotics, including olanzapine, can produce unwanted metabolic side effects, weight gain and diabetes. However, neuronal correlates of change related to food information processing have not been investigated with these medications. We studied the effect of a pharmacological manipulation with an antipsychotic known to cause weight gain on metabolites, cognitive tasks and neural correlates related to food regulation. We used functional magnetic resonance imaging in conjunction with a task requiring visual processing of appetitive stimuli in schizophrenic patients and healthy controls before and after 16 weeks of antipsychotic medication with olanzapine. In patients, the psychological and neuronal changes associated following the treatment correlated with appetite control measures and metabolite levels in fasting blood samples. After 16 weeks of olanzapine treatment, the patients gained weight, increased their waist circumference, had fewer positive schizophrenia symptoms, a reduced ghrelin plasma concentration and an increased concentration of triglycerides, insulin and leptin. In premotor area, somatosensory cortices as well as bilaterally in the fusiform gyri, the olanzapine treatment increased the neural activity related to appetitive information in schizophrenic patients to similar levels relative to healthy individuals. However, a higher increase in sensitivity to appetitive stimuli after the treatment was observed in insular cortices, amygdala and cerebellum in schizophrenic patients as compared with healthy controls. Furthermore, these changes in neuronal activity correlated with changes in some metabolites and cognitive measurements related to appetite regulation

Self-supervised Outdoor Scene Relighting

Outdoor scene relighting is a challenging problem that requires good understanding of the scene geometry, illumination and albedo. Current techniques are completely supervised, requiring high quality synthetic renderings to train a solution. Such renderings are synthesized using priors learned from limited data. In contrast, we propose a self-supervised approach for relighting. Our approach is trained only on corpora of images collected from the internet without any user-supervision. This virtually endless source of training data allows training a general relighting solution. Our approach first decomposes an image into its albedo, geometry and illumination. A novel relighting is then produced by modifying the illumination parameters. Our solution capture shadow using a dedicated shadow prediction map, and does not rely on accurate geometry estimation. We evaluate our technique subjectively and objectively using a new dataset with ground-truth relighting. Results show the ability of our technique to produce photo-realistic and physically plausible results, that generalizes to unseen scenes.Comment: Published in ECCV '20, http://gvv.mpi-inf.mpg.de/projects/SelfRelight

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

The voltage dependence of the TMEM16B/anoctamin2 calcium-activated chloride channel is modified by mutations in the first putative intracellular loop

Ca(2+)-activated Cl(-) channels (CaCCs) are involved in several physiological processes. Recently, TMEM16A/anoctamin1 and TMEM16B/anoctamin2 have been shown to function as CaCCs, but very little information is available on the structure-function relations of these channels. TMEM16B is expressed in the cilia of olfactory sensory neurons, in microvilli of vomeronasal sensory neurons, and in the synaptic terminals of retinal photoreceptors. Here, we have performed the first site-directed mutagenesis study on TMEM16B to understand the molecular mechanisms of voltage and Ca(2+) dependence. We have mutated amino acids in the first putative intracellular loop and measured the properties of the wild-type and mutant TMEM16B channels expressed in HEK 293T cells using the whole cell voltage-clamp technique in the presence of various intracellular Ca(2+) concentrations. We mutated E367 into glutamine or deleted the five consecutive glutamates (386)EEEEE(390) and (399)EYE(401). The EYE deletion did not significantly modify the apparent Ca(2+) dependence nor the voltage dependence of channel activation. E367Q and deletion of the five glutamates did not greatly affect the apparent Ca(2+) affinity but modified the voltage dependence, shifting the conductance-voltage relations toward more positive voltages. These findings indicate that glutamates E367 and (386)EEEEE(390) in the first intracellular putative loop play an important role in the voltage dependence of TMEM16B, thus providing an initial structure-function study for this channel. \ua9 2012 Cenedese et al