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245 results for “Mathematics”
Technical Debt in Mathematical Programming Dataset
<p>The replication package includes the complete survey structure and the email invitation (with the Qualtrics' embedded fields). The participant collection sheet used for the convenience sample is shared empty, to disclose the data that was collected; note that we cannot provide the completed sheet (which included name, email and affiliation of invited participants) because we are restricted by our Ethical Protocol to preserve the participant's identity. This is a problem known as the `privacy vs utility paradox' (Li et al., 2009), and its study was out of scope for this investigation.</p>
Sensitivity analysis of a mathematical model simulating the post-hepatectomy hemodynamics response
<p>Recently a lumped-parameter model of the cardiovascular system was proposed to simulate the hemodynamics response to partial hepatectomy and evaluate the risk of portal hypertension (PHT) due to this surgery. Model parameters are tuned based on each patient data. This work focuses on a global sensitivity analysis (SA) study of such model to better understand the main drivers of the clinical outputs of interest. The analysis suggests which parameters should be considered patient-specific and which can be assumed constant without losing in accuracy in the predictions. While performing the SA, model outputs need to be constrained to physiological ranges. An innovative approach exploits the features of the polynomial chaos expansion method to reduce the overall computational cost. The computed results give new insights on how to improve the calibration of some model parameters. Moreover the final parameter distributions enable the creation of a virtual population available for future works. Although this work is focused on partial hepatectomy, the pipeline can be applied to other cardiovascular hemodynamics models to gain insights for patient-specific parameterization and to define a physiologically relevant virtual population.</p>
Supplementary Materials of "Elementary mathematics helps to shed light on the transpiration budget under water stress"
<p>This directory contains the Jupyter notebook used to do complete analysis from our paper "Elementary mathematics sheds light on the transpiration budget under water stress" submitted to the Ecohydrology Journal at the Special Issues "ECOHYDROLOGY OF INLAND AND COASTAL WATERS in honor of Ignacio Rodriguez-Iturbe".</p> <p>These materials are referenced in the main text and supplemental text of the publication. The purpose of this repository is to facilitate replication of our analysis by any interested parties. </p> <p>Specifically, this directory contains ten files:</p> <ul> <li>From 0 to 5, Jupyter Notebook prepared and used for the analysis (please execute the notebooks in numerical sequence). </li> <li>"Table_S1.xlsx" Data From: Kröber, W., H. Heklau, and H. Bruelheide. 2015. “Leaf Morphology of 40 Evergreen and Deciduous Broadleaved Subtropical Tree Species and Relationships to Functional Ecophysiological Traits.” Plant Biology 17 (2): 373–83. <a href="https://doi.org/10.1111/plb.12250"><span>https://doi.org/10.1111/plb.12250</span></a>.</li> <li>"Richards_VG.csv" contains Van Genuchten Parameters for various soils.</li> <li>"The_Rosetta_Stone_of_the_Darcy_Buckingham_law.pdf" addresses the challenge of converting water flux units between Darcy-like soil and plant descriptions, where hydrologists use "head" units (meters) and plant physiologists use pressure potential (MPa). The aim is to clarify and perform the necessary unit conversions, with detailed explanations available in the relevant section on <a href="https://abouthydrology.blogspot.com/2022/10/my-water-management-in-agricolture.html"><span>this webpage</span></a>.</li> </ul>
Data from: Digital twin mathematical models suggest individualized hemorrhagic shock resuscitation strategies
<p><strong>Background:</strong> Optimizing resuscitation to reduce inflammation and organ dysfunction following human trauma-associated hemorrhagic shock is a major clinical hurdle. This is limited by the short duration of pre-clinical studies and the sparsity of early data in the clinical setting.</p> <p><strong>Methods:</strong> We sought to bridge this gap by linking preclinical data in the porcine model with clinical data from patients from the Prospective, Observational, Multicenter, Major Trauma Transfusion (PROMMTT) study via a three-compartment ordinary differential equation model of inflammation and coagulation.</p> <p><strong>Results:</strong> The model accurately predicts physiologic, inflammatory, and laboratory measures in both the porcine model and patients, as well as the outcome and time of death in the PROMMTT cohort. Model simulation suggests that resuscitation with plasma and red blood cells outperformed resuscitation with crystalloid or plasma alone, and that earlier plasma resuscitation reduced injury severity and increased survival time.</p> <p><strong>Conclusions:</strong> This workflow may serve as a translational bridge from pre-clinical to clinical studies in trauma-associated hemorrhagic shock and other complex disease settings.</p>
Brain Functors: A mathematical model of intentional perception and action-Figure 15: Mathematical butterfly diagram for a brain functor
<p>HomA(F(X),A) ≅ Het(X,A) ≅ HomX(X,G(A)). If the functor F also has a left adjoint H : A→X, then: HomX(H(A),X) ≅ Het(A,X) ≅ HomA(A,F(X)). Then taking the isomorphisms that do not involve G or H gives:<br> and Het(A,X) ≅ HomA(A,F(X)), i.e., F is a brain functor. Hence all functors that have both right and left adjoints are brain functors.<br> 16<br> HomA(F(X),A) ≅ Het(X,A)</p>
Figure 14: Adjunctive square diagram-Brain Functors: A mathematical model of intentional perception and action
<p>Finally, a brain functor is a functor F: X→A that is a left semiadjunction for Het(X, A) and a right semiadjunction for Het(A, X), i.e., HomA(F(X),A) ≅ Het(X,A)<br> and Het(A,X) ≅ HomA(A,F(X)).<br> For each d in Het(X, A), there is a unique hom f(d) in HomA(F(X), A) so that the upper triangular ‘wing’ in the butterfly diagram commutes. For each d' in Het(A, X), there is a unique hom g(d') in HomA(A, F(X)) so that the lower triangular ‘wing’ commutes.</p>
Figure 13: Composition of hets and homs-Brain Functors: A mathematical model of intentional perception and action
<p>The cross-category object-to-object hets d : X→A will be indicated by thin arrows (→) rather than thick arrows (⇒). The first question is how do heteromorphisms compose with one another? But that is not necessary. Chimera do not need to ‘mate’ with other chimera to form a ‘species’ or category; they only need to mate with the intra-category morphisms on each side to form other chimera.8 Given a het d : X→A from an object in a category X to an object in a category A, and homs h : X'⇒X in X and k : A⇒A' in A, the composition dh : X'⇒X→A is another het X'→A and the composition kd : X→A⇒A' is another het X→A'.</p>
Figure 12: Language faculty as two-way determination through a universal-Brain Functors: A mathematical model of intentional perception and action
<p>A brain functor, broadly put, is any universal mechanism of determination that can factor determination either way through a universal–rather than an adjunction that factors one way determination through two (receiving and sending) universals. In some contexts in the life sciences, determination is strictly one way so one might expect to find a semiadjunction but not a two-way system like a brain functor. An application of the scheme for a brain functor in the cognitive sciences is to model the language faculty where there is two way determination between vocal stimuli and internal representations. The previous semiadjunctions for language understanding and language action can be merged to arrive at the brain-like function of the language faculty.</p>
Figure 11: Coding and decoding Cartesian coordinates of geometrical points-Brain Functors: A mathematical model of intentional perception and action
<p>The simplest form of a brain "functor" is just a two-way representation or coding system that constructs and implements a set of codes. Given some set of objects, it is encoded using some isomorphic set of representations or codes for the objects, and then given an instance of the code, it is decoded to determine the object. Coordinatizing is a form of coding. The geometrical plane is a collection of points, and the Cartesian coordinate system represents each point P by a pair (xP, yP) of coordinates. Given a point P , the "coordinate" function selects the coordinates (xP, yP) of the point which is the recognized or coded output, and given the coordinates or code for a point (xP, yP) as an input, the "plot" function designates the point.</p>
Figure 8: Language production through a sending universal-Brain Functors: A mathematical model of intentional perception and action
<p>The dual to "language understanding" is language production or linguistic action (e.g., "speech acts"). The role of the specific het is played by some auditory output such as utterances (Humboldt’s "vocal stimulus"). But the corresponding internal specific hom is the speech act (i.e., internal speech with intentionality) that through the language faculty produces the same outputs but as intentional speech.</p>
Figure 1: Het d: X→ A-Brain Functors: A mathematical model of intentional perception and action
<p>In the body of this paper, I will try to keep the mathematics at a minimal conceptual level– which the mathematical formulations restricted to the Appendix. Category theory lends itself to visualization in diagrams so that non-mathematical style of presentation is emphasized by an abundant use of diagrams. A category is intuitively a set of objects of the same type. Morphisms between objects should be thought of as a type of determining relation or cause-effect relation between the objects. When a morphism is between objects of the same category, it is called a homomorphism or hom, and when between objects of different categories it is a heteromorphism or het.4 One of the problems in the conventional treatment of category theory5 is that it tries to ignore heteromorphisms even though hets are a natural part of working mathematics. This leads to certain definitions being rather contrived (to avoid mentioning hets), the usual treatment of the universal mapping properties in adjunctions being the case in point. Adjunctions will be introduced informally and in the natural manner using hets. The general setting is how the objects in one category (e.g., the "environment" in a life sciences context), the "sending" category, will "affect" or "determine" objects in another category (e.g., "organisms"), the "receiving" category. We start with an object X in the sending category, an object A in the receiving category, and a specific het determination d : X → A from X to A.6</p>
Figure 4: The Adjunctive Square Diagram-Brain Functors: A mathematical model of intentional perception and action
<p>Dually, we can define the above situation, given by the association of the sending universal G(A) with each object A in the receiving category along with the canonical isomorphism Het(X,A) ≅ Homsending(X,G(A)), as a right semiadjunction. Now we are prepared to define an adjunction essentially as:<br> adjunction = left semiadjunction + right semiadjunction Homreceiving(F(X),A) ≅ Het(X,A) ≅ Homsending(X,G(A)).</p>
Figure 7: -"Action" as determination through a sending universal-Brain Functors: A mathematical model of intentional perception and action
<p>Dual to the generic model of "perception" is the generic model of "action"–which is the determinative scheme given by a right semiadjunction. In the model of perception, there is the uninterpreted message as just a sensory input (the external het), and then there is the second level where the factorization (the internal hom) through the receiving universal recognizes the interpretation, meaning, or intentionality of the message. In the dual model of "action," the external het specifies the external behavior (which could be even a reflex behavior) while internal hom factoring through a sending universal that supplies the "intentionality" of the "action" (where an "action" is a "behavior" plus the second level of "intentionality"). In each case, we end up with a certain behavior but determined by two different means.</p>
Figure 6: "Perception" as determination through a receiving universal-Brain Functors: A mathematical model of intentional perception and action
<p>Before turning to right semiadjunctions, it might be useful to present a rather generic version of determination through a receiving universal as model of "recognition" or "perception" that captures many of the common features of the various examples. The determination through the receiving universal is the active internal process that supplies the "interpretation" or "intentionality" to the raw sense data. The red blotch is seen as a tomato; the sound "ya" is understood as indicating agreement, and so forth. In the passive/direct alternative, the raw sensory input supplies Lockean "perception" like writing on a blank slate or a stamp making an impression on wax.</p>
Figure 3: Scheme for determination by a sending universal G(A)-Brain Functors: A mathematical model of intentional perception and action
<p>The universal mapping property is: for every het d : X→A, there is a unique hom g(d) : X⇒G(A) in the sending category such that: eAg(d) = X⇒G(A)→A = X→A = d i.e., such that the determination through the universal sending het eA : G(A)→A preceded by the hom g(d) : X⇒G(A) is the same as the original het d : X→A.</p>
Mathematics Stack Exchange API Q&A Data
<p>This dataset was compiled as part of the ESPRC project "Example-driven machine-human collaboration in mathematics", for the purpose of doing text-based analysis of mathematical discourse and for the construction of a conversational mathematics bot.</p> <p>It consists of approximately 1 million mathematics questions and their respective answers, as well as markers of interaction quality (such as user-provided scoring of question and answer quality) and social dynamics (reputation scores, badges, etc).</p> <p>The data was obtained from the <a href="https://stackexchange.com/">StackExchange</a> website, by querying the <a href="https://api.stackexchange.com/">Stack Exchange API</a> according to its documentation.</p> <p> </p> <p> </p>
Figure 16 in Mathematical interpretation of avian egg shapes
Figure 16. Ovoid curves: a) Hügelschäffer (according to Obradovic et al., 2013); b) Blaschke (according to Köller, 2000); с) Schauberger (according to Coats, 2001).
Figure 15 in Mathematical interpretation of avian egg shapes
Figure 15. Yamamoto oval (а) (according to Yamamoto, 2020); Cartesian oval (b) (according to Köller, 2000); Möller oval (c) (according to Möller, 2009).
Figure 13 in Mathematical interpretation of avian egg shapes
Figure 13. Cone-like ovoids: a) zeta-curve (Stadnicki, 2015); b) Phalacrocorax carbo; c) Anser anser; d) Phalacrocorax pelagicus; e) Grus canadensis; f) Grus grus.
Figure 14 in Mathematical interpretation of avian egg shapes
Figure 14. Cartesian ovals: а) with p = 1, q = 2 and c = 5; b) with p = 1, q = 3 and c = 5 (Beverlin, 2006); с) hyperbolic cone (Kirsh, 2010).
ScienceDex guides
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These curated guides explain access requirements, typical timelines, costs, and reuse considerations for widely used research datasets.
Allen Brain Atlas
Allen Brain Atlas is an Allen Institute collection of brain map atlases, datasets, APIs, and analysis tools covering mouse, human, and non-human primate brain resources.
Annotated Behaviour and Observability Dataset (ABODe)
ABODe is a University of Edinburgh DataShare dataset for behavior classification in group-housed mice using home-cage video, identities, bounding boxes, ground-plate positions, and annotator labels.
DANDI Archive for NWB datasets
DANDI is a BRAIN Initiative archive for publishing and sharing neurophysiology data, including electrophysiology, optophysiology, and behavioral data packaged as NWB and related standards.
International Brain Laboratory public data
The International Brain Laboratory public data releases expose standardized mouse decision-making experiments, including Neuropixels recordings, widefield calcium imaging, behavior, and session metadata accessed through the ONE API.
OpenNeuro
OpenNeuro is a free, open platform for sharing neuroimaging datasets, with public search, dataset pages, and download paths for web, S3, DataLad, and the OpenNeuro CLI.