Search

Rationale Two distinct subphenotypes have been identified in acute respiratory distress syndrome (ARDS), but the presence of subgroups in ARDS associated with COVID-19 is unknown. The objective of this study was to identify clinically relevant, novel subgroups in COVID-19-related ARDS, and compare them to previously described ARDS subphenotypes. Methods Eligible participants were adults with COVID-19 and ARDS at Columbia University Irving Medical Center. Latent class analysis (LCA) was used to identify subgroups with baseline clinical, respiratory, and laboratory data serving as partitioning variables. A previously-developed machine learning model was used to classify patients as the hypoinflammatory and hyperinflammatory subphenotypes. Baseline characteristics and clinical outcomes were compared between subgroups. Heterogeneity of treatment effect (HTE) for corticosteroid-use in subgroups was tested. Measurements and Main Results From 3/2-4/30/2020, 483 patients with COVID-19-related ARDS met study criteria. A two-class LCA model best fit the population (p=0.0075). Class 2 (23%) had higher pro-inflammatory markers, troponin, creatinine and lactate, lower bicarbonate and lower blood pressure than Class 1 (77%). 90-day mortality was higher in Class 2 versus Class 1 (75% vs 48%; p

We investigate E *-dense semi\-groups as analogues of E-dense semigroups for semigroups with zero. We give a characterisation theorem for E *-dense semigroups whose idempotents form a *-rectangular band. The construction methods of generalised Rees matrix semigroups are employed to provide examples and illustrations. Our results are analogous to those of Weipoltshammer for E-dense semigroups.

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance.

People have difficulty reasoning with diagnostic information in uncertain situations, especially when an understanding and calculation of inverse conditional probabilities (Bayes theorem) is required. While natural frequency representations of inference tasks improve matters, they suffer from three problems: (1) calculation errors persist with a majority of subjects; (2) the representation suffers from an illusion of certainty that ignores ambiguity; and (3) the costs of repeatedly applying the representation to deal with imprecision and ambiguity in inference are prohibitive. We describe a user friendly, interactive, graphical software tool for calculating, visualizing, and communicating accurate inferences about uncertain states when relevant diagnostic test information (sensitivity, specificity, and base rate) is both imperfect and ambiguous in its application to a specific patient. The software is free, open-source, and runs on all popular PC operating systems (Windows, Mac, Linux).

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders., This is a completely reorganized and rewritten version of our earlier paper math/0701313v2, with a number of new results

We consider the question of membership of A ∨ G, where A and G are the pseudovarieties of finite aperiodic semigroups, and finite groups, respectively. We find a straightforward criterion for a semigroup S lying in a class of finite semigroups that are weakly abundant, to be in A ∨ G. The class of weakly abundant semigroups contains the class of regular semigroups, but is much more extensive; we remark that any finite monoid with semilattice of idempotents is weakly abundant. To study such semigroups we develop a number of techniques that may be of interest in their own right.

We show that the free weakly E-ample monoid on a set X is a full submonoid of the free inverse monoid FIM(X) on X. Consequently, it is ample, and so coincides with both the free weakly ample and the free ample monoid FAM(X) on X. We introduce the notion of a semidirect product Y*T of a monoid T acting doubly on a semilattice Y with identity. We argue that the free monoid X* acts doubly on the semilattice [Formula: see text] of idempotents of FIM(X) and that FAM(X) is embedded in [Formula: see text]. Finally we show that every weakly E-ample monoid has a proper ample cover.

The construction by Hall of a fundamental orthodox semigroup W B from a band B provides an important tool in the study of orthodox semigroups. Hall's semigroup W B has the property that a semigroup is fundamental and orthodox with band of idempotents isomorphic to B if and only if it is embeddable as a full subsemigroup into W B . The aim of this article is to extend Hall's approach to some classes of nonregular semigroups. From a band B, we construct a semigroup U B that plays the role of W B for a class of weakly B-abundant semigroups having a band of idempotents B. The semigroups we consider, in particular U B , must also satisfy a weak idempotent connected condition. We show that U B has subsemigroup V B where V B satisfies a stronger notion of idempotent connectedness, and is again the canonical semigroup of its kind. In turn, V B contains W B as its subsemigroup of regular elements. Thus we have the following inclusions as subsemigroups: either of which may be strict, even in the finite case. The ex...

Epoxy casts were created of five naturally occurring fractures in dolostone and aperture distribution was measured using a light attenuation method. The optically determined aperture matrices showed a skew towards smaller apertures, with the larger models demonstrating a lognormal distribution and the smaller models a normal distribution. Surface variograms of each display a significant degree of anisotropy. The models had spatial correlation ranges between 1.8 and 5 cm. The optical mean aperture, mean hydraulic aperture and mass-balance aperture were all determined. In addition, the coefficient of variation (C v) and anisotropy ratio (AR) for each model was determined to compare their predictions with the actual tracer behavior in each of the models. In all cases, the hydraulically determined mean aperture was the same order of magnitude as the optically determined mean aperture. The mass-balance-derived mean aperture differed significantly from the optical mean aperture based on the degree of channeling in the model. However, neither the C v nor the AR correlated well to the actual behavior of the tracers, suggesting they are insufficient to predict void connectivity. Overall the epoxy replicas performed moderately well and can be well characterized for use in studies where visualization is of primary importance.

If $A$ is a stable basis algebra of rank $n$, then the set $S_{n-1}$ of endomorphisms of rank at most $n-1$ is a subsemigroup of the endomorphism monoid of $A$. This paper gives a number of necessary and sufficient conditions for $S_{n-1}$ to be generated by idempotents. These conditions are satisfied by finitely generated free modules over Euclidean domains and by free left $T$-sets of finite rank, where $T$ is cancellative monoid in which every finitely generated left ideal is principal.

By using translucent epoxy replicas of natural single fractures, it is possible to optically measure aperture distribution and directly observe NAPL flow. However, detailed characterization of epoxy reveals that it is not a sufficiently good analogue to natural rock for many two-phase flow studies. The surface properties of epoxy, which is hydrophobic, are quite unlike those of natural rock, which is generally assumed to be hydrophilic. Different surface wettabilities result in dramatically different two-phase flow behavior and residual distributions. In hydrophobic replicas, the NAPL flows in well-developed channels, displacing water and filling all of the pore space. In hydrophilic replicas, the invading NAPL is confined to the largest aperture pathways and flow frequently occurs in pulses, with no limited or no stable channel development, resulting in isolated blobs with limited accessible surface area. The pulsing and channel abandonment behaviors described are significantly different from the piston-flow frequently assumed in current modeling practice. In addition, NAPL never achieved total saturation in hydrophilic models, indicating that significantly more than a monolayer of water was bound to the model surface. Despite typically only 60-80% NAPL saturation, there was generally good agreement between theoretically calculated Young-Laplace aperture invasion boundaries and the observed minimum apertures invaded. The key to determining whether surface wettability is negligible, or not, lies in accurate characterization of the contaminant-geologic media system under study. As long as the triple-point contact angle of the system is low (20 degrees), the assumption of perfect water wettability is not a bad one.

Proper ample monoids are described by means of a certain category acted upon on both sides by a cancellative monoid. Making use of this characterization, we show that every ample monoid $S$ has a proper ample cover, which can be taken to be finite whenever $S$ is finite.

A left ample semigroup is a semigroup with a unary operation + which has a (2,1)-algebra embedding into a symmetric inverse monoid I(X), the operation + on I(X) being defined by α+ = αα-1. We consider some analogues for left ample semigroups of results on E-unitary covers of inverse semigroups due to McAlister and Reilly. The analogue of an E-unitary cover is a proper cover, and we discuss the construction of proper covers in terms of relational homomorphisms, and of dual prehomomorphisms. We observe that our construction gives an E-dense proper cover for an E-dense left ample semigroup. We also consider proper covers constructed from strict embeddings into factorisable left ample monoids. In contrast to the inverse case, not all proper covers arise in this way. However, in the E-dense case, we characterise those E-dense proper covers which can be constructed from such embeddings.

Rapid increases in the swine (Sus scrofa domestica) population in the 1990s and associated potential for nitrate N pollution of surface waters led the state of North Carolina to adopt stringent waste management regulations in 1993. Our objectives were to characterize (i) nitrate N movement from waste application fields (WAFs) in shallow ground water, and (ii) soil, hydrologic, and biological factors influencing the amount of nitrate N in the adjacent stream. A ground water monitoring study was conducted for 36 mo on a swine farm managed under new regulations. Water table contours and lack of vertical gradients indicated horizontal flow over most of the site. Nitrate N concentrations in water from shallow wells in WAFs averaged 30 +/- 19 mg L(-1) and delta15N ratios for nitrate N were between +20 and +25 per mil. Nitrate N concentration decreased from field-edge to streamside wells by 22 to 99%. Measurement of delta18O and delta15N enrichment of nitrate in ground water throughout the WAF-riparian system indicated that denitrification has not caused significant 15N enrichment of nitrate. Over a 24-mo period, delta15N ratios for nitrate N in the stream approached delta15N ratios for nitrate N in ground water beneath WAFs indicating delivery of some waste-derived nitrate N to the stream in shallow ground water. Nitrate N concentrations in the stream were relatively low, averaging 1 mg L(-1). Dilution of high nitrate N water in shallow horizontal flow paths with low nitrate N water from deeper horizontal flow paths at or near the stream, some denitrification as ground water discharges through the stream bottom, and some denitrification in riparian zone contributed to this low nitrate N concentration.

Fountain, Gould and Smith introduced the concept of equivalence of orders in a semigroup and the notion of a maximal order. We examine these ideas in the context of orders in completely 0-simple semigroups with particular emphasis on abundant orders.

We give an abstract description of the kernel of a proper primitive inverse congruence on a categorical semigroup. More specifically, we show that it is a *-reflexive, *-unitary, *-dense subsemigroup, and that on a given categorical semigroup there is a one–one correspondence between such subsemigroups and the proper primitive inverse congruences. Our results allow us to give a description of the minimum proper primitive inverse semigroup congruence on a strongly E*-dense categorical semigroup.

This paper uses a two‐dimensional graphical technique to provide a constructive proof of Arrow's impossibility theorem. Students (and instructors) of intermediate microeconomics should have no problem in following the graphical proof developed here. The meaning of the condition of independence of irrelevant alternatives and its function in Arrow's theorem become transparent in this proof.

We obtain analogues, in the setting of semigroups with zero, of McAlister's convering theoren and the structure theorems of McAlister, O'Carroll, and Margolis and Pin. The covers come from a class C of semigroups defined by modifying one of the many characterisations of E-unitary inverse semigroups, namely, that an inverse semigroups is E-unitary if and only if it is an inverse image of an idempotent-pure homomorphism onto a group. The class C is properly contained in the class of all E*-unitary inverse semigroups introduced by Szendrei but properly contains the class of strongly categorical E*-unitary semigroups recently considered by Gomes and Howie.

Munn's construction of a fundamental inverse semigroup T E from a semilattice E provides an important tool in the study of inverse semigroups. We present here a semigroup F E that plays for a class of E -semiadequate semigroups the role that T E plays for inverse semigroups. Every inverse semigroup with semilattice of idempotents E is E -semiadequate. There are however many interesting E -semiadequate semigroups that are not inverse, we consider various such examples arising from Schutzenberger products.

Inspired by the ring theory concepts of orders and classical rings of quotients, Fountain and Petrich introduced the notion of a completely 0-simple semigroup of quotients in [19]. This was generalised to a much wider class of semigroups by Gould in [20]. The notion extends the well known concept of group of quotients [8]. To give the definition we first have to explain what is meant by a square-cancellable element in a semigroup. Let a be an element of a semigroup S. We say that a is square-cancellable in S if for all x, y ∈ S, xa = ya implies that xa = ya

The relation [Rtilde] on a monoid S provides a natural generalisation of Green’s relation R. If every [Rtilde]-class of S contains an idempotentS is left semiabundant; if [Rtilde] is a left congruence then S satisfies(CL). Regular monoids, indeed left abundant monoids, are left semiabundant and satisfy(CL). However, the class of left semiabundant monoids is much larger, as we illustrate with a number of examples. This is the first of three related papers exploring the relationship between unipo-tent monoids and left semiabundancy. We consider the situations where the power enlargement or the Szendrei expansion of a monoid yields a left semiabundant monoid with(CL). Using the Szendrei expansion and the notion of the least unipotent monoid congruence σ on a monoid S, we construct functors is a left adjoint of F σ. Here U is the category of unipotent monoids and F is a category of left semiabundant monoids with properties echoing those of F-inverse monoids.

In 1966, J. M. Howie characterized the self-maps of a set which can be written as a product (i.e., composite) of idempotent self-maps of that set. Using a wreath product construction introduced by V. Fleischer, the first-named author was recently able to describe products of idempotent endomorphisms of a freeS-act of finite rank whereS is any monoid. The purpose of the present paper is to extend this result to freeS-acts of infinite rank.

Surfactant enhanced aquifer remediation (SEAR) is an attractive alternative to traditional pump and treat methods for remediating aquifers contaminated with nonaqueous phase liquids. However, initial studies indicate that the application of surfactant can reduce aquifer permeability by more than an order of magnitude, limiting the efficiency of SEAR. A series of column experiments using mixtures of medium sand and montmorillonite clay demonstrate that existing permeability reduction models for biofouling and deep-bed filtration poorly predict surfactant induced permeability reductions. An alternative permeability reduction model is proposed which is based on the assumption that the sorbed surfactant effectively increases the volume fraction of the clay. The model is shown to reasonably predict observed permeability reductions, particularly for clay fractions less than 20%. A numerical simulation of surfactant transport that incorporates the effective clay fraction model demonstrates that induced permeability reductions significantly influence the transport of surfactant through an aquifer.

A semigroup with zero isidempotent bounded (IB) if it is the 0-direct union of idempotent generated principal left ideals and the 0-direct union of idempotent generated principal right ideals. Notable examples are completely 0-simple semigroups and the wider class of primitive abundant semigroups. Significant to the structure of these semigroups is that they are all categorical at zero. In this paper we describe IB semigroups that are categorical at zero in terms ofdouble blocked Rees matrix semigroups. This generalises Fountain's characterisation of primitive abundant semigroups via blocked Rees matrix semigroups [1], which in turn yields the Rees theorem for completely 0-simple semigroups.

Let X be an infinite set and T ( X ) be the full transformation semigroup on X . In [4] and [6] Howie gives a description of the subsemigroup of T ( X ) generated by its idempotents. In order to do this he defines, for α in T ( X ), and refers to the cardinals s (α) = | S (α)|, d (α) = | Z (α)| and | c (α) = |C(α)| as the shift , the defect , and the collapse of α respectively. Then putting he proves that the subsemigroup of T ( X ) generated by its idempotents is . Furthermore, both F and Q are generated by their idempotents

This is the second in a series of papers that develops the theory of reflection monoids, motivated by the theory of reflection groups. Reflection monoids were first introduced in arXiv:0812.2789. In this paper we study their presentations as abstract monoids. Along the way we also find general presentations for certain join-semilattices (as monoids under join) which we interpret for two special classes of examples: the face lattices of convex polytopes and the geometric lattices, particularly the intersection lattices of hyperplane arrangements. Another spin-off is a general presentation for the Renner monoid of an algebraic monoid, which we illustrate in the special case of the "classical" algebraic monoids., Comment: 41 pages

The relation ℛ* is defined on a semigroup S by the rule that ℛ*b if and only if the elements a, b of S are related by the Green's relation ℛ in some oversemigroup of S. A semigroup S is an E-semigroup if its set E(S)of idempotents is a subsemilattice of S. A left adequate semigroup is an E-semigroup in which every ℛ*-class contains an idempotent. It is easy to see that, in fact, each ℛ*-class of a left adequate semigroup contains a unique idempotent [2]. We denote the idempotent in the ℛ*-class of a by a+.

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task, and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other, and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance.

Subjective probabilities play a role in many economic decisions. There is a large theoretical literature on the elicitation of subjective probabilities, and an equally large empirical literature. However, there is a gulf between the two. The theoretical literature proposes a range of procedures that can be used to recover subjective probabilities, but stresses the need to make strong auxiliary assumptions or "calibrating adjustments" to elicited reports in order to recover the latent probability. With some notable exceptions, the empirical literature seems intent on either making those strong assumptions or ignoring the need for calibration. We illustrate how the joint estimation of risk attitudes and subjective probabilities using structural maximum likelihood methods can provide the calibration adjustments that theory calls for. This allows the observer to make inferences about the latent subjective probability, calibrating for virtually any well-specified model of choice under uncertainty. We demonstrate our procedures with experiments in which we elicit subjective probabilities. We calibrate the estimates of subjective beliefs assuming that choices are made consistently with expected utility theory or rank-dependent utility theory. Inferred subjective probabilities are significantly different when calibrated according to either theory, thus showing the importance of undertaking such exercises. Our findings also have implications for the interpretation of probabilities inferred from prediction markets.

Suppose you are interested in the level of a state variable (e.g. a disease is present or absent or of a pre-specified level of severity, or a failure is recorded or not, etc.) and have a potentially useful but imperfect diagnostic test method, (e.g. a blood test result for this disease, or a quality control check for manufacturing defects, is either definitely positive or not). How do you interpret the result of the diagnostic test for the level of the state variable when some or all of the information underlying the inference is ambiguous (imprecise)? This publication for the Wolfram Demonstration project is designed to facilitate the "what-if" exploration of the effects of ambiguities (imprecision) in sensitivity, specificity, and base rate information, alone or in combination, on posterior inferences through a linked tabular natural frequency and graphical probability format representation of underlying uncertainties. The textual description explains the underlying theory of boundedly rational inference. An appendix contains the full Mathematica code used to implement the interactive software that implements and explains the underlying theory.

Products of idempotents are investigated in the endomorphism monoid of an algebra belonging to a class of algebras which includes finite sets and finite dimensional vector spaces as special cases. It is shown that every endomorphism which is not an automorphism is a product of idempotent endomorphisms. This provides a common generalisation of earlier results of Howie and Erdos for the cases when the algebra is a set or vector space respectively.

SynopsisAn alternative proof of a theorem which characterises orders in semiprime rings with minimal condition is given. The approach used is to make use of the corresponding result for prime rings and is inspired by Herstein's proof of Goldie's theorem on orders in semisimple Artinian rings.

Let E denote the set of non-identity idempotent matrices in the full matrix ring Mn(R) over a principal ideal domain R. A necessary and sufficient condition is found for the subsemigroup generated by E to be the set of all matrices in Mn(R) of rank less than n. The condition is satisfied when R is a discrete valuation ring and when R is the ring of integers. Thus every n × n matrix of rank less than n is a product of idempotent integer matrices.

The relation ℒ* is defined on a semigroup S by the rule that a ℒ*b if and only if the elements a, b of S are related by Green's relation ℒ in some oversemigroup of S. A semigroup S is an E-semigroup if its set E(S) of idempotents is a subsemilattice of S. A right adequate semigroup is an E-semigroup in which every ℒ*-class contains an idempotent. It is easy to see that, in fact, each ℒ*-class of a right adequate semigroup contains a unique idempotent [8]. We denote the idempotent in the ℒ*-class of a by a*. Then we may regard a right adequate semigroup as an algebra with a binary operation of multiplication and a unary operation *. We will refer to such algebras as *-semigroups. In [10], it is observed that viewed in this way the class of right adequate semigroups is a quasi-variety.

Urbanization of rural farmland is a pervasive trend around the globe, and maintaining and protecting adequate water supplies in suburban areas is a growing problem. Identification of the sources of groundwater contamination in urbanized areas is problematic, but will become important in areas of rapid population growth and development. The isotopic composition of NO3 (delta15N(NO3) and delta18O NO3), NH4 (delta15N(NH4)), groundwater (delta2H(wt) and delta18O(wt)) and chloride/bromide ratios were used to determine the source of nitrate contamination in drinking water wells in a housing development that was built on the site of a dairy farm in the North Carolina Piedmont, U.S. The delta15N(NO3) and delta18O NO3 compositions imply that elevated nitrate levels at this site in drinking well water are the result of waste contamination, and that denitrification has not significantly attenuated the groundwater nitrate concentrations. delta15N(NO3) and delta18O(NO3) compositions in groundwater could not differentiate between septic effluent and animal waste contamination. Chloride/ bromide ratios in the most contaminated drinking water wells were similar to ratios found in animal waste application fields, and were higher than Cl/Br ratios observed in septic drain fields in the area. delta18O(wt) was depleted near the site of a buried waste lagoon without an accompanying shift in delta2H(wt) suggesting water oxygen exchange with CO2. This water-CO2 exchange resulted from the reduction of buried lagoon organic matter, and oxidation of the released gases in aerobic soils. delta18O(wt) is not depleted in the contaminated drinking water wells, indicating that the buried dairy lagoon is not a source of waste contamination. The isotope and Cl/Br ratios indicate that nitrate contamination in these drinking wells are not from septic systems, but are the result of animal waste leached from pastures into groundwater during 35 years of dairy operations which did not violate any existing regulations. Statutes need to be enacted to protect the health of the homeowners that require well water to be tested prior to the sale of homes built on urbanized farmland.

Let LS denote the language of (right) S-sets over a monoid S and let ∑ S be a set of sentences in LS which axiomatises S-sets. A general result of model theory says that ∑ S has a model companion, denoted by TS , precisely when the class E of existentially closed S-sets is axiomatisable and in this case, TS axiomatises E . It is known that TS exists and is stable if and only if S is right coherent. In the study of stable first order theories, superstable and totally transcendental theories are of particular interest. We describe types over TS algebraically and use our result to confirm that TS is stable. We prove that TS is superstable if and only if S satisfies the maximal condition for right ideals. The situation for total transcendence is more complicated but a usable result is obtained for the case where U -rank coincides with Morley rank.

Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or empty, then so does the graph product. Our second main result gives a presentation for the inverse hull of such a graph product. We then specialise to the case of the inverse hulls of graph monoids, obtaining what we call polygraph monoids. Among other properties, we observe that polygraph monoids are F*-inverse. This follows from a general characterisation of those right cancellative monoids with inverse hulls that are F*-inverse., 24 pages

In the terminology of Birget and Rhodes [3], an expansion is a functor F from the category of semigroups into some special category of semigroups such that there is a natural transformation η from F to the identity functor for which η s is surjective for every semigroup S . The three expansions introduced in [3] have proved to be of particular interest when applied to groups. In fact, as shown in [4], Ĝ (2) are isomorphic for any group G , is an E -unitary inverse monoid and the kernel of the homomorphism η G is the minimum group congruence on . Furthermore, if G is the free group on A , then the “cut-down to generators” which is a subsemigroup of is the free inverse semigroup on A . Essentially the same result was given by Margolis and Pin [12].