A Note on the Welfare Gap in Fair Ordering

In this short note, we show a gap between the welfare of a traditionally 'fair' ordering, namely first-in-first-out (an ideal that a number of blockchain protocols strive to achieve), where the first transactions to arrive are the ones put into the block, and an 'optimal' inclusion that is, at least approximately, welfare-maximizing, such as choosing which transactions are included in a block via an auction. We show this gap is positive under a simple model with mild assumptions where we assume transactions are, roughly speaking, uniformly drawn from a reasonable distribution

Ranking Causal Influence of Financial Markets via Directed Information Graphs

A non-parametric method for ranking stock indices according to their mutual causal influences is presented. Under the assumption that indices reflect the underlying economy of a country, such a ranking indicates which countries exert the most economic influence in an examined subset of the global economy. The proposed method represents the indices as nodes in a directed graph, where the edges' weights are estimates of the pair-wise causal influences, quantified using the directed information functional. This method facilitates using a relatively small number of samples from each index. The indices are then ranked according to their net-flow in the estimated graph (sum of the incoming weights subtracted from the sum of outgoing weights). Daily and minute-by-minute data from nine indices (three from Asia, three from Europe and three from the US) were analyzed. The analysis of daily data indicates that the US indices are the most influential, which is consistent with intuition that the indices representing larger economies usually exert more influence. Yet, it is also shown that an index representing a small economy can strongly influence an index representing a large economy if the smaller economy is indicative of a larger phenomenon. Finally, it is shown that while inter-region interactions can be captured using daily data, intra-region interactions require more frequent samples.Comment: To be presented at Conference on Information Sciences and Systems (CISS) 201

The Specter (and Spectra) of Miner Extractable Value

Miner extractable value (MEV) refers to any excess value that a transaction validator can realize by manipulating the ordering of transactions. In this work, we introduce a simple theoretical definition of the 'cost of MEV', prove some basic properties, and show that the definition is useful via a number of examples. In a variety of settings, this definition is related to the 'smoothness' of a function over the symmetric group. From this definition and some basic observations, we recover a number of results from the literature

The Geometry of Constant Function Market Makers

Constant function market makers (CFMMs) are the most popular type of decentralized trading venue for cryptocurrency tokens. In this paper, we give a very general geometric framework (or 'axioms') which encompass and generalize many of the known results for CFMMs in the literature, without requiring strong conditions such as differentiability or homogeneity. One particular consequence of this framework is that every CFMM has a (unique) canonical trading function that is nondecreasing, concave, and homogeneous, showing that many results known only for homogeneous trading functions are actually fully general. We also show that CFMMs satisfy a number of intuitive and geometric composition rules, and give a new proof, via conic duality, of the equivalence of the portfolio value function and the trading function. Many results are extended to the general setting where the CFMM is not assumed to be path-independent, but only one trade is allowed. Finally, we show that all 'path-independent' CFMMs have a simple geometric description that does not depend on any notion of a 'trading history'

Bounds on Efficiency Metrics in Photonics

In this paper, we present a method for computing bounds for a variety of efficiency metrics in photonics. We focus on the special case where the objective function can be written as the ratio of two quadratic functions of the field and show that there exists a simple semidefinite programming relaxation for this problem. We provide a numerical example of bounding the maximal mode conversion purity for a device of given size. This paper is accompanied by an open source implementation

matbesancon/MathOptSetDistances.jl: v0.2.8

<h2>MathOptSetDistances v0.2.8</h2> <p><a href="https://github.com/matbesancon/MathOptSetDistances.jl/compare/v0.2.7...v0.2.8">Diff since v0.2.7</a></p> <p><strong>Merged pull requests:</strong></p> <ul> <li>Add projection to scaled set (#71) (@blegat)</li> <li>Fix add_constraint with nonzero constant in function (#72) (@blegat)</li> <li>Refactor unvec_symm into reshape (#73) (@blegat)</li> <li>Use import as syntax (#74) (@blegat)</li> <li>Return Symmetric matrix in reshape_vector (#75) (@blegat)</li> <li>vec_symm -> vectorize (#76) (@blegat)</li> <li>Fix RotatedSecondOrderCone NormedEpigraphDistance (#78) (@odow)</li> </ul&gt

Enhancing endogenous stem cells in the newborn via delayed umbilical cord clamping

There is currently no consensus among clinicians and scientists over the appropriate or optimal timing for umbilical cord clamping. However, many clinical studies have suggested that delayed cord clamping is associated with various neonatal benefits including increased blood volume, reduced need for blood transfusion, increased cerebral oxygenation in pre-term infants, and decreased frequency of iron deficiency anemia in term infants. Human umbilical cord blood contains significant amounts of stem and progenitor cells and is currently used in the treatment of several life-threatening diseases. We propose that delayed cord clamping be encouraged as it enhances blood flow from the placenta to the neonate, which is accompanied by an increase supply of valuable stem and progenitor cells, as well as may improve blood oxygenation and increase blood volume, altogether reducing the infant′s susceptibility to both neonatal and age-related diseases

Mannitol-Enhanced Delivery of Stem Cells and Their Growth Factors across the Blood–Brain Barrier

Ischemic brain injury in adults and neonates is a significant clinical problem with limited therapeutic interventions. Currently, clinicians have only tPA available for stroke treatment and hypothermia for cerebral palsy. Owing to the lack of treatment options, there is a need for novel treatments such as stem cell therapy. Various stem cells including cells from embryo, fetus, perinatal, and adult tissues have proved effective in preclinical and small clinical trials. However, a limiting factor in the success of these treatments is the delivery of the cells and their by-products (neurotrophic factors) into the injured brain. We have demonstrated that mannitol, a drug with the potential to transiently open the blood–brain barrier and facilitate the entry of stem cells and trophic factors, as a solution to the delivery problem. The combination of stem cell therapy and mannitol may improve therapeutic outcomes in adult stroke and neonatal cerebral palsy