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Abstract Background In patients undergoing high-risk surgery, it is recommended to titrate fluid administration using stroke volume or a dynamic variable of fluid responsiveness (FR). However, this strategy usually requires the use of a hemodynamic monitor and/or an arterial catheter. Recently, it has been shown that variations of central venous pressure (ΔCVP) during an alveolar recruitment maneuver (ARM) can predict FR and that there is a correlation between CVP and peripheral venous pressure (PVP). This prospective study tested the hypothesis that variations of PVP (ΔPVP) induced by an ARM could predict FR. Methods We studied 60 consecutive patients scheduled for high-risk abdominal surgery, excluding those with preoperative cardiac arrhythmias or right ventricular dysfunction. All patients had a peripheral venous catheter, a central venous catheter and a radial arterial catheter linked to a pulse contour monitoring device. PVP was always measured via an 18-gauge catheter inserted at the antecubital fossa. Then an ARM consisting of a standardized gas insufflation to reach a plateau of 30 cmH2O for 30 s was performed before skin incision. Invasive mean arterial pressure (MAP), pulse pressure, heart rate, CVP, PVP, pulse pressure variation (PPV), and stroke volume index (SVI) were recorded before ARM (T1), at the end of ARM (T2), before volume expansion (T3), and one minute after volume expansion (T4). Receiver-operating curves (ROC) analysis with the corresponding grey zone approach were performed to assess the ability of ∆PVP (index test) to predict FR, defined as an ≥ 10% increase in SVI following the administration of a 4 ml/kg balanced crystalloid solution over 5 min. Results ∆PVP during ARM predicted FR with an area under the ROC curve of 0.76 (95%CI, 0.63 to 0.86). The optimal threshold determined by the Youden Index was a ∆PVP value of 5 mmHg (95%CI, 4 to 6) with a sensitivity of 66% (95%CI, 47 to 81) and a specificity of 82% (95%CI, 63 to 94). The AUC’s for predicting FR were not different between ΔPVP, ΔCVP, and PPV. Conclusion During high-risk abdominal surgery, ∆PVP induced by an ARM can moderately predict FR. Nevertheless, other hemodynamic variables did not perform better.

We equip the type A diagrammatic Hecke category with a special derivation, so that after specialization to characteristic p it becomes a p-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the p-dg Grothendieck group. We conjecture that the p-dg Grothendieck group is isomorphic to the Iwahori-Hecke algebra, equipping it with a basis which may differ from both the Kazhdan-Lusztig basis and the p-canonical basis. More precise conjectures will be found in the sequel. Here are some other results contained in this paper. We provide an incomplete proof of the classification of all degree +2 derivations on the diagrammatic Hecke category, and a complete proof of the classification of those derivations for which the defining relations of the Hecke algebra are satisfied in the p-dg Grothendieck group. In particular, our special derivation is unique up to duality and equivalence. We prove that no such derivation exists in simply-laced types outside of finite and affine type A. We also examine a particular Bott-Samelson bimodule in type A_7, which is indecomposable in characteristic 2 but decomposable in all other characteristics. We prove that this Bott-Samelson bimodule admits no nontrivial fantastic filtrations in any characteristic, which is the analogue in the p-dg setting of being indecomposable. [ABSTRACT FROM AUTHOR]

We prove that many of the recently-constructed algebras and categories which appear in categorification can be equipped with an action of sl2 by derivations. The sl2 representations which appear are filtered by tensor products of coVerma modules. In a future paper, we will address the implications of the sl2 structure for categorification. [ABSTRACT FROM AUTHOR]

In the Negev Desert ecosystems, flint-stone cover on slopes acts as a barrier against water flow. As a result, soil moisture increases and organic matter accumulates under the stone and in the immediate surroundings, both affecting the duration of soil microbial activity. On the other hand, during the dry season (characterized by approximately 210 dew nights), flint-stone cover plays an important role in the formation of dew, which eventually trickles down beneath the stone, correspondingly enhancing biological activity. The present study examined the possible role of flint stones as hotspots for soil microbial-community activity and diversity. The results were compared with those obtained from the adjacent stone-free soils in the open spaces (OS), which served as controls. Microbial activity (respiration and biomass) and functional diversity were determined by the MicroRespTM method. In addition, estimates of genetic diversity and viable counts of bacteria and fungi [colony-forming units (CFUs)] were obtained. The soil was significantly wetter and contained more organic matter beneath the flint stones (BFS). As hypothesized, biological activity was enhanced under the stones, as described by CO2 evolution, microbial-community biomass functional diversity, and fungal phylogenetic diversity. BFS environments favored a greater range of catabolic functions. Taxa generally known for their stress resilience were found in the OS habitats. The results of this study elucidate the importance of flint-stone cover to soil microbial biomass, community activity, and functional diversity in the northern Negev Desert.

We enlarge a Coxeter group into a category, with one object for each finite parabolic subgroup, encoding the combinatorics of double cosets. This category, the singular Coxeter monoid, is connected to the geometry of partial flag varieties. Our main result is a presentation of this category by generators and relations. We also provide a new description of reduced expressions for double cosets. We describe all the braid relations between such reduced expressions, and prove an analogue of Matsumoto's theorem. This gives a proper development of ideas first introduced by Geordie Williamson. In type A$A$, we also equip the singular Coxeter monoid with a diagrammatic presentation using webs. [ABSTRACT FROM AUTHOR]

Copyright of Annales Mathematiques Blaise Pascal is the property of Laboratoire mathematiques Blaise Pascal - CNRS UMR 6620 and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we give a version of Bergman's diamond lemma which applies to certain monoidal categories presented by generators and relations. In particular, it applies to: the Coxeter presentation of the symmetric groups, the quiver Hecke algebras of Khovanov-Lauda-Rouquier, the Webster tensor product algebras, and various generalizations of these. We also give an extension of Manin-Schechtmann theory to non-reduced expressions. [ABSTRACT FROM AUTHOR]

We prove the relative hard Lefschetz theorem for Soergel bimodules. It follows that the structure constants of the Kazhdan-Lusztig basis are unimodal. We explain why the relative hard Lefschetz theorem implies that the tensor category associated by Lusztig to any two-sided cell in a Coxeter group is rigid and pivotal. [ABSTRACT FROM AUTHOR]

The monoidal category of Soergel bimodules is an incarnation of the Hecke category, a fundamental object in representation theory. We present this category by generators and relations, using the language of planar diagrammatics. We show that Libedinsky's light leaves give a basis for morphism spaces and give a new proof and a generalization of Soergel's classification of the indecomposable Soergel bimodules. [ABSTRACT FROM AUTHOR]

Let R be the polynomial ring in n variables, acted on by the symmetric group Sn. Soergel constructed a full monoidal subcategory of R-bimodules which categorifies the Hecke algebra, whose objects are now known as Soergel bimodules. Soergel bimodules can be described as summands of Bott-Samelson bimodules (attached to sequences of simple reflections), or as summands of generalized Bott-Samelson bimodules (attached to sequences of parabolic subgroups). A diagrammatic presentation of the category of Bott-Samelson bimodules was given by the author and Khovanov in previous work. In this paper, we extend it to a presentation of the category of generalized Bott-Samelson bimodules. We also diagrammatically categorify the representations of the Hecke algebra which are induced from trivial representations of parabolic subgroups. The main tool is an explicit description of the idempotent which picks out a generalized Bott-Samelson bimodule as a summand inside a Bott-Samelson bimodule. This description uses a detailed analysis of the reduced expression graph of the longest element of Sn, and the semi-orientation on this graph given by the higher Bruhat order of Manin and Schechtman. This paper relies extensively on color figures. Some references to color may not be meaningful in the printed version, and we refer the reader to the online version which includes the color figures. [ABSTRACT FROM AUTHOR]

We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group $W$. The (two-colored) Temperley–Lieb category is embedded inside this category as the degree $0$ morphisms between color-alternating objects. The indecomposable Soergel bimodules are the images of Jones–Wenzl projectors. When $W$ is infinite, the parameter $q$ of the Temperley–Lieb algebra may be generic, yielding a quantum version of the geometric Satake equivalence for $\mathfrak{sl}_{2}$. When $W$ is finite, $q$ must be specialized to an appropriate root of unity, and the negligible Jones–Wenzl projector yields the Soergel bimodule for the longest element of $W$. [ABSTRACT FROM AUTHOR]

Using the diagrammatic calculus for Soergel bimodules developed by B. Elias and M. Khovanov, we show that Rouquier complexes are functorial over braid cobordisms. We explicitly describe the chain maps which correspond to movie move generators. [ABSTRACT FROM AUTHOR]

The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of planar graphs, which categorifies the Temperley-Lieb algebra. Certain ideals appearing in this quotient are related both to the 1- skeleton of the Coxeter complex and to the topology of 2D cobordisms. We demonstrate how further subquotients of this category will categorify the irreduciblemodules of the Temperley-Lieb algebra. [ABSTRACT FROM AUTHOR]