Mathematical Constraints Research Articles

Fast charging sodium-ion batteries based on Te-P-C composites and insights to low-frequency limits of four common equivalent impedance circuits

Various tellurium-red phosphorus-carbon (Te-P-C) composites with different Te to P ratios were prepared via high-energy mechanical milling for application as anode materials in sodium-ion batteries. Highly conductive Te was added to increase the electrical conductivity and improve the mechanical strength of the P-C composite. The optimized Te-P-C (1:2) composite exhibited a reversible capacity of 593 mAh g−1, demonstrating a capacity retention of 82% at the 100th cycle in the fast recharge test (3 A g−1). This performance is related to the electrochemical impedance of each composite. Te-P-C composites are sufficiently simple, such that new constraints for the composites, provided by electrochemical impedance spectroscopy (EIS) results, can be examined. Four mathematical constraints for four frequently applied equivalent circuits at low-frequency limits were declared for batteries. The linear dependence of the sum of the real and imaginary parts of the impedance (Zreal + Zimag) on the frequency was used to interpret the systems. The newly proposed restrictions significantly reduced the uncertainty of the charge-transfer resistance (Rct) for the Te-P-C composites; the corrected nominal value (158 Ω to 188 Ω) of Rct was more reliable than the uncorrected one (125 Ω to 560 kΩ from commercial fitting software). Therefore, it is believed that the four proposed constraints could provide a simple and convenient way (linear regression) for electrochemical engineers to control the reliability of the interpretation of EIS data in battery systems.

Detecting Outlier Patterns With Query-Based Artificially Generated Searching Conditions

In the age of social computing, finding interesting network patterns or motifs is significant and critical for various areas, such as decision intelligence, intrusion detection, medical diagnosis, social network analysis, fake news identification, and national security. However, subgraph matching remains a computationally challenging problem, let alone identifying special motifs among them. This is especially the case in large heterogeneous real-world networks. In this article, we propose an efficient solution for discovering and ranking human behavior patterns based on network motifs by exploring a user's query in an intelligent way. Our method takes advantage of the semantics provided by a user's query, which in turn provides the mathematical constraint that is crucial for faster detection. We propose an approach to generate query conditions based on the user's query. In particular, we use meta paths between the nodes to define target patterns as well as their similarities, leading to efficient motif discovery and ranking at the same time. The proposed method is examined in a real-world academic network using different similarity measures between the nodes. The experiment result demonstrates that our method can identify interesting motifs and is robust to the choice of similarity measures.

Beyond Bias: Artificial Intelligence and Social Justice

Artificial intelligence (AI) systems can discriminate against protected classes — a fact that has sparked an extensive literature about bias in AI. Bias, as important as it is, is a special case of the overall problem of social justice. Beyond Bias focuses on the general problem. It incorporates contributions from the extensive discussion of AI and fairness in the computer science literature. In particular, it draws on Fairness Through Awareness, an influential article by the Harvard computer scientist Cynthia Dwork and her co-authors. Adapting Dwork’s approach, Beyond Bias reexpresses intuitive, well-motivated fairness constraints in a more mathematical way that shows how to apply the constraints to mathematically and computationally complex AI systems. The mathematics nonetheless uses only elementary arithmetic (unlike Dwork et al.). Beyond Bias adapts the fairness constraints that it reexpresses from the Yale economist John Roemer. As Roemer notes in Equality of Opportunity, a conception of “equality of opportunity . . . prevalent today in Western democracies . . . says that society should do what it can to ‘level the playing field’ among individuals who compete for positions.” Beyond Bias shows that AI systems can unfairly tilt the playing field. The reason lies in the pervasive (and unavoidable) use of “proxy variables” — e. g., using credit ratings to predict driving safety (as many insurance companies do). The credit ratings are the substitute — the proxy — for details about individuals’ driving practices. Beyond Bias is the first article to apply a level playing field concept of fairness to issues of fairness in AI systems. Beyond Bias briefly reviews the history of the use of proxy variables to evaluate consumers from the late Nineteenth Century to the present. It was already clear at the close of the Nineteenth Century that proxy-driven analysis could make seemingly unrelated aspects of one’s life “have a profound impact on [one’s] future potential in matters economic or social,” as Dan Bouk notes in HOW OUR DAYS BECAME NUMBERED: RISK AND THE RISE OF THE STATISTICAL INDIVIDUAL. The concern was that proxy-driven analysis would unfairly tilt the playing field, and that concern continues to this day. Beyond Bias outlines a regulatory approach that ensures level playing field fairness by incorporating its mathematical constraints on AI systems.

Codon optimization by 0-1 linear programming

The problem of choosing an optimal codon sequence arises when synthetic protein-coding genes are added to cloning vectors for expression within a non-native host organism: to maximize yield, the chosen codons should have a high frequency in the host genome, but particular nucleotide bases sequences (called “motifs”) should be avoided or, instead, included. Dynamic programming (DP) has successfully been used in previous approaches to this problem. However, DP has a computational limit, especially when long motifs are forbidden, and does not allow control of motif positioning and combination. We reformulate the problem as an integer linear program (IP) and show that, with the same computational resources, one can easily solve problems with much more nucleotide bases and much longer forbidden/desired motifs than with DP. Moreover, IP (i) offers more flexibility than DP to treat constraints/objectives of different nature, and (ii) can efficiently deal with newly discovered critical motifs by dynamically re-optimizing additional variables and mathematical constraints.

Impact of heated triangular ribs on hydrodynamic forces in a rectangular domain with heated elliptic cylinder: Finite element analysis

Abstract The heat transfer in flowing liquid stream towards confined geometries having natural or man-made obstacles offers complex mathematical constraints at the heated body-liquid stream interface. Therefore, to appraise the heat transfer in liquid stream with installed obstacles particularly in terms of hydrodynamic forces remains a topic of great interest for the researchers. Owing such interest, the present article contains the extended evaluation of hydrodynamic forces in a flowing liquid stream with heat transfer individualities. To be more, the Newtonian liquid stream is initiated with the parabolic velocity profile at an inlet of partially heated rectangular channel. The heated elliptic shaped cylinder is placed fixed in between channel as an obstacle. The heated triangular ribs are installed case-wise namely (i) channel without ribs (ii) heated triangular rib at lower wall (iii) heated triangular rib at upper wall (iv) heated triangular rib at both upper and lower walls. The presence of heated triangular ribs as an obstacles modifies the endpoint conditions and hence the developed flow narrating differential system cannot be solved exactly. Therefore, the most trustful numerical method named finite element method with LBB-stable finite element pair is utilized to report acceptable solution in terms of streamlines and isotherms contour plots. The hydrodynamic forces are evaluated for each case by adopting line integration around outer surface of heated elliptic obstacle. It is noticed that when the heated triangular rib is installed on both upper and lower channel walls, the drag coefficient is found considerably high.

The Design of Urban Traffic in Ferizaj through Operational Research

Cities are undergoing rapid changes continuously due to the high demands of this era, and simultaneously affect several life fields, namely urban transport. High demands are triggering people to travel more frequently than ever; thus, they utilize public transportation more and private transportation less as the latter ceased to fulfill all the transportation needs. Thus, public transportation demand has been increasing greatly alongside citizens’ needs. Nonetheless, many cities lack proper urban traffic planning and organization, while some lack an urban transport service. Ferizaj, a city in Kosovo, is one of the cities that lacks an urban traffic designation; hence, this paper presents a designed urban traffic model, precisely suitable to fulfill the urban transportation need for Ferizaj city. This model is designed under the utilization of applied mathematics’ techniques and operational research. Several factors have been considered, following the geographical distribution of the population, existing roads, and residents’ needs. Consequently, the Solver program has been used as an optimization tool to find the shortest path and most economical paths, added in the discussion part. Besides, the likelihood of the designed urban traffic model’s application in Ferizaj is discussed, considering its viability and application conditions. This study presents mathematical constraints to design a model of the bus network in Ferizaj through Solver. We have used mathematical optimization methods, graph theory, the simulation model through the Solver computer program for network minimal distances and presenting the first model of the Urban traffic network in Ferizaj.

Previsão da demanda por viagens domiciliares através de método sequencial baseado em população sintética e redes neurais artificiais

A estimativa de viagens por domicílio é fundamental para a tomada de decisões relativas ao planejamento de transportes. Porém, para obter essa estimativa são necessários dados desagregados dos domicílios, que geralmente são obtidos pela Pesquisa Domiciliar de Origem e Destino. No entanto, a maioria das cidades enfrenta problemas para a aquisição desses dados, uma vez que este tipo de pesquisa é de alto custo de preparação e execução. Desta forma, surge a necessidade de ferramentas que forneçam dados confiáveis e com baixo custo. Assim, o objetivo deste artigo é apresentar um método sequencial, para estimativa de viagens domiciliares, a partir de população sintética e Redes Neurais Artificiais (RNAs). A população sintética foi baseada em dados agregados do censo e simulação Monte Carlo. Os resultados obtidos com as RNAs foram comparados aos resultados de um modelo linear tradicional, mostrando-se melhores e corroborando o potencial do uso de RNAs para modelagem da demanda por transportes. As viagens sintéticas por domicílio foram validadas a partir dos dados desagregados da Pesquisa Origem-Destino (2007) e testes de hipótese para comparação de valores típicos e distribuições populacionais. Em 71% dos setores censitários, as viagens sintéticas foram consideradas similares aos dados reais, confirmando a eficiência do método proposto. Assim, a principal lacuna desta pesquisa, é a apresentação do método sequencial, capaz de tanto minimizar problemas de aquisição de dados quanto atenuar as restrições e suposições matemáticas, inerentes aos modelos tradicionais de demanda por transportes.

Exact Spectral Moments and Differentiability of the Weierstrass-Mandelbrot Fractal Function

Abstract Fractal mathematics using the Weierstrass-Mandelbrot (WM) function has spread to many fields of science and engineering. One of these is the fractal characterization of rough surfaces, which has gained ample acceptance in the area of contact mechanics. That is, a single mathematical expression (the WM function) contains characteristics that mimic the appearance of roughness. Moreover, the “roughness” is “similar” across large dimension scales ranging from macro to nano. The field of contact mechanics is largely divided into two schools of thought: (1) the roughness of real surfaces is essentially random, for which stochastic treatment is appropriate, and (2) surface roughness can be reduced to fractal mathematics using fractal parameters. Under certain mathematical constraints, the WM function is either stochastic or deterministic. The latter has the appeal that it contains no randomness, so fractal mathematics may offer closed-form solutions. Spectral moments of rough surfaces still apply to both approaches, as these represent physical metrology properties of the surface standard deviation, slope, and curvature. In essence, spectral moments provide a means of data reduction so that other physical processes can subsequently be applied. It is well known, for example, that the contact model of rough surfaces, by Greenwood and Williamson (GW), depends on parameters that are direct outcomes of these moments. Despite the vast amount of publications on the WM function dedicated to surfaces, two papers stand out as originators, where the others mostly rework their results. These two papers, however, contain some omissions and approximations that may lead to gross errors in the estimation of the spectral moments. The current work revisits these papers and adds information, but departs in the mathematical treatment to derive exact expressions for the said moments. Moreover, it is said that the WM function is nondifferential. That is also revisited herein, as another approach to derive the spectral moments depends on such derivatives. First, the complete mathematical treatment of the WM function is made, then the spectral moments are derived to yield exact forms, and finally, examples are given where the physical meanings of the approximate and exact moments are discussed and their values are compared. Numerical procedures will be introduced for both, and the effectiveness of the computational effort is discussed. One numerical procedure is particularly effective for any digitized signal, whether that originates from analytical functions (e.g., WM) or real surface measurements.

A New 3-D Minimum Cost Flow Phase Unwrapping Algorithm Based on Closure Phase

Phase unwrapping (PU) is a critical step in interferometric synthetic aperture radar (InSAR) processing chain, which can directly affect the quality of the final results. In order to improve the accuracy and robustness of PU algorithm, especially for the interferograms that have relatively long perpendicular baselines, in this article, we propose a new 3-D minimum cost flow (MCF) algorithm based on closure phase. Different from current 3-D PU algorithms that aim to solve the unwrapped phase gradients (UPGs) among different interferograms and usually follow a 1+2D mode, this new approach establishes a mathematical constraint within the closure phases and unwraps them jointly. This constraint is based on a prior knowledge that the sums of UPGs, where the UPGs are in the azimuth/range plane whereas belongs to different interferograms in the closure phase, can be obtained before PU. The main advantage of this new approach is that neither a temporal deformation model nor a preliminary atmospheric phase calibration is required before PU. Besides, this new approach combines the MCF model and phase consistency, showing advantages in reducing the chance of phase aliasing. We implement our new approach in both continuous and discrete interferograms and use real SAR data to validate the performance by comparing with the 2-D MCF algorithm in SNAPHU and the 3-D PU algorithm in StaMPS.

A NMF-based extraction of physically meaningful components from sensory data of metal casting processes

The paper introduces a novel approach for the extraction of physically meaningful thermal component time series during the manufacturing of casting parts. We treat their extraction as Blind Source Separation (BSS) problem by exploiting process-related prior knowledge. Our proposed method arranges temperature time series into a data matrix, which is then decomposed by Non-negative Matrix Factorization (NMF). The latter is guided by a knowledge-based strategy, which initializes the NMF component matrix with time curves designed according to basic physical processes. The temperature time series encompass exclusively non-negative data. Hence NMF lends itself a natural choice as it does not impose mathematical constraints that lack any immediate physical interpretation. We show how to extract components linked to physical phenomena that typically occur during production and cannot be monitored directly. We apply our method to real world data, collected in a foundry during the series production of casting parts for the automobile industry and demonstrate its efficiency.

A machine learning approach for classification of equivalent mutants

AbstractMutation testing is a fault‐based technique to test the quality of test suites by inducing artificial syntactic faults or mutants in a source program. However, some mutants have the same semantics as original program and cannot be detected by any test suite input known as equivalent mutants. Equivalent mutant problem (EMP) is undecidable as it requires manual human effort to identify a mutant as equivalent or killable. The constraint‐based testing (CBT) theory suggests the use of mathematical constraints which can help reveal some equivalent mutants using mutant features. In this paper, we consider three metrics of CBT theory, ie, reachability, necessity, and sufficiency to extract feature constraints from mutant programs. Constraints are extracted using program dependency graphs. Other features such as degree of significance, semantic distance, and information entropy of mutants are also extracted to build a binary classification model. Machine learning algorithms such as Random Forest, GBT, and SVM are applied under two application scenarios (split‐project and cross‐project) on ten Java programs to predict equivalent mutants. The analysis of the study demonstrates that that the proposed techniques not only improves the efficiency of the equivalent mutant detection but also reduces the effort required to perform it with small accuracy loss.

HOW MANY MOLECULAR MECHANISMS MUST BE ALTERED SIMULTANEOUSLY TO SLOW AGING AND EXTEND LIFESPAN?

Most anti-aging therapeutics are designed to target single molecules, single molecular mechanisms, or single cell types. Yet, to produce a substantial lifespan extension, these interventions would need to act promiscuously and delay the onset of many or all causes of death. In invertebrate models, several molecular-level interventions are known to act this way, yet their downstream action on multiple causes of death remains poorly understood. Recently, we identified a strong mathematical constraint in the way that many different interventions in aging alter all-cause mortality in the nematode Caenorhabditis elegans. Interventions including suppression of IGF/insulin signaling, disruption of the hsf-1 heat shock factor and the hif-1 hypoxia-inducible factor, as well as changes in diet and body temperature, all produce a temporal scaling of lifespan. This temporal scaling suggests a common physiologic path through which diverse, evolutionary-conserved, molecular mechanisms can simultaneously influence all causes of death.

UMAP reveals cryptic population structure and phenotype heterogeneity in large genomic cohorts.

Human populations feature both discrete and continuous patterns of variation. Current analysis approaches struggle to jointly identify these patterns because of modelling assumptions, mathematical constraints, or numerical challenges. Here we apply uniform manifold approximation and projection (UMAP), a non-linear dimension reduction tool, to three well-studied genotype datasets and discover overlooked subpopulations within the American Hispanic population, fine-scale relationships between geography, genotypes, and phenotypes in the UK population, and cryptic structure in the Thousand Genomes Project data. This approach is well-suited to the influx of large and diverse data and opens new lines of inquiry in population-scale datasets.

Two‐stage stochastic operation framework for optimal management of the water–energy–hub

This study proposes a bi-level stochastic framework to address optimal scheduling of energy hub (EH) in a pool-based short-term market considering electrical–thermal–water demands. EH acts as an independent price-maker producer in a day-ahead electricity market aiming to maximise its profit. The market settlement mechanism is constructed as the pay-at-market-clearing price (MCP), where each producer/consumer is paid at the MCP. The problem model is formulated as a bi-level optimisation approach in a stochastic environment, in which the upper level defines the profit maximisation of the proposed strategic producer, whereas the lower-level expresses the dispatch cost of the considered power grid. This results in a problem formulation with mathematical equilibrium constraints which is transformed into a new mixed-integer linear programme based on Karush–Kuhn–Tucker conditions. A stochastic framework based on unscented transform is developed to model the high uncertainties of EH water demand, EH thermal demand, EH electric demand, generators and loads submitted price to the market. The simulation results on the IEEE test system advocate the effectiveness and appropriate performance of the proposed strategic EH producer in the electricity market and its effect on the locational marginal prices of buses in a transmission-constrained market.

Constraints imposed by zero-crossing invariance on cochlear models with two mechanical degrees of freedom.

The zero crossings of basilar-membrane (BM) responses to clicks are nearly independent of stimulus intensity. This work explores the constraints that this invariance imposes on one-dimensional nonlinear cochlear models with two degrees of freedom (2DoF). The locations of the poles and zeros of the BM admittance, calculated for a set of linear models in which the strength of the active force is progressively decreased, provides a playground for evaluating the behavior of a corresponding nonlinear model at increasing stimulus levels. Mathematical constraints on the model parameters are derived by requiring that the poles of the admittance move horizontally in the s-plane as the active force is varied. These constraints ensure approximate zero-crossing invariance over a wide stimulus level range in a nonlinear model in which the active force varies as a function of the local instantaneous BM displacement and velocity. Two different 2DoF models are explored, each capable of reproducing the main qualitative characteristics of the BM response to tones (i.e., the tall and broad activity pattern at low stimulus levels, the large gain dynamics, and the partial decoupling between gain and phase). In each model, the motions of the two masses are compared with response data from animal experiments.

Towards Automatic Mathematical Exercise Solving

Knowledge graphs are widely applied in many applications. Automatically solving mathematical exercises is also an interesting task which can be enhanced by knowledge reasoning. In this paper, we design MathGraph, a knowledge graph aiming to solve high school mathematical exercises. Since it requires fine-grained mathematical derivation and calculation of different mathematical objects, we design a crowdsourcing-based method to help build MathGraph. MathGraph supports massive kinds of mathematical objects, operations and constraints which may be involved in exercises. Furthermore, we propose an algorithm to align a semantically parsed exercise to MathGraph and figure out the answer automatically. Extensive experiments on real-world datasets verify the effectiveness of MathGraph.

Robust Seismic Image Interpolation with Mathematical Morphological Constraint.

Seismic image interpolation is a currently popular research subject in modern reflection seismology. The interpolation problem is generally treated as a process of inversion. Under the compressed sensing framework, various sparse transformations and low-rank constraints based methods have great performances in recovering irregularly missing traces. However, in the case of regularly missing traces, their applications are limited because of the strong spatial aliasing energies. In addition, the erratic noise always poses a serious impact on the interpolation results obtained by the sparse transformations and low-rank constraints-based methods. This is because the erratic noise is far from satisfying the statistical assumption behind these methods. In this study, we propose a mathematical morphology-based interpolation technique, which constrains the morphological scale of the model in the inversion process. The inversion problem is solved by the shaping regularization approach. The mathematical morphological constraint (MMC)-based interpolation technique has a satisfactory robustness to the spatial aliasing and erratic energies. We provide a detailed algorithmic framework and discuss the extension from 2D to higher dimensional version and the back operator in the shaping inversion. A group of numerical examples demonstrates the successful performance of the proposed technique.

Pinch Methods for Efficient Use of Water in Food Industry: A Survey Review

The implementation of sustainable water management practices, through the recycling and reuse of water, is essential in terms of minimizing production costs and the environmental impact of the food industry. This problem goes beyond the classical audit and housekeeping practices through developing a systemic water-using reduction strategy. The implementation of such an approach needs R&D development, especially for the food industry, where there is a lack of knowledge on: (a) process integration and (b) data on the pollutant indicators or (c) volumes of water used and discharged at specific steps of the food processing line. Since energy pinch analysis emerged, different variations of pinch methods have been developed. As a variation of pinch, Water pinch analysis is a global and systematic approach to minimize water consumption and discharges, especially for the most energy-intensive and water-consuming factories. Based on the nature of the food industry, the real systems are complex, multi-source multi-contaminant systems, the problem should be well formulated, including mathematical constraints (inequalities thresholds). Current work has reviewed comprehensive literature about different variations of pinch analysis. In continue, water pinch method deeply discussed and some relevant data concerning the water using process and pollutant indicators have been reviewed with emphasis on the food industry sector.

A Machine-Learning Methodology Using Domain-Knowledge Constraints for Well-Data Integration and Well-Production Prediction

Summary In this paper, we propose a machine–learning methodology using domain–knowledge constraints for well–data integration, prior/expert–knowledge incorporation, and sweet–spot identification. Such methodology enables the analysis of the effects of the main variables involved in production prediction and the evaluation of what–if scenarios of production prediction within geological zones. This methodology will allow streamlining the process of data integration, analytics and machine learning for better decisions, saving time, and helping geologists and reservoir and completion engineers in the task of sweet–spot identification and completion design. We tested the proposed methodology with production, completions, and petrophysical data from a field within a geological target zone. For instance, using local Kriging, we estimated gamma ray features from gamma ray measurements from vertical and horizontal wells, and we integrated those features into the production– and completion–well data, generating an integrated data set for machine–learning modeling. Besides the usual black–box machine–learning models, we used generalized additive models (GAMs) and shape–constraint additive models (SCAMs) for predictive modeling. Those models permit the incorporation of prior/expert knowledge in terms of interaction terms and mathematical constraints on the shape of the effect of the covariates, such as petrophysical and completion parameters, resulting in greater accuracy and interpretability of the predicted production vs. classical black–box machine–learning modeling. We also defined hypothetical what–if scenarios of oil production, such as by estimating the empirical distributions of production estimates using hypothetical settings for completions within the region of interest.

Error-correcting codes and information in biology

Shannon's channel coding theorem (1948), a major result of information theory, paradoxically states that errorless communication is possible using an unreliable channel. Since then, engineers developed many error-correcting codes and decoding algorithms. A performance close to the predicted one was eventually achieved no earlier than the beginning of the nineties. Many communication facilities would not exist without error-correcting codes, e.g., mobile telephony and terrestrial digital television. This article explains first how they work without mathematical formalism. An error-correcting code is a minority subset among some set of messages. Within this subset, the messages are sufficiently different from each other to be exactly identified even if a number of their symbols, up to a certain limit, are changed. Beyond this limit, another message can be erroneously identified. An error-correcting code is interpreted as a set of messages subjected to constraints which make their symbols mutually dependent. Although mathematical constraints are conveniently used in engineering, constraints of any other kind, possibly of natural origin, can generate error-correcting codes.Biologists implicitly assume that genomes were conserved during the geological ages, without realizing that this is impossible without error-correcting means. Symbol errors occur during replication of a genome; chemical reactions and radiations are other sources of errors. Their number increases with time in the absence of correction. A genomic code will exactly regenerate the genome provided its decoding is attempted after a short enough time interval. If the number of errors is too large, however, the decoded genome will differ from the initial one and a mutation will occur. Periodically attempted decodings thus will conserve a genome except for very infrequent mutations if decoding attempts are frequent enough. The better conservation of very ancient parts of genomes, like the HOX genes, cannot be explained unless assuming that a genomic error-correcting code resulting from a stepwise encoding exists: a first encoding was followed later by a second one where a new information and the result of the first encoding were jointly encoded, and this process was repeated several times, eventually resulting in an overall code made of nested components where the older is an information, the better it is protected. Organic codes in Barbieri's meaning result from the same process and have the same structure. Any new organic code induces new genomic constraints, hence new components in a nested system of codes. Organic codes may thus be identified with the system of nested error-correcting codes needed to conserve the genetic information.A majority of biologists deny that information theory can be useful to them. It is shown on the contrary that the living world cannot be understood if the scientific concept of information is ignored. Heredity makes the present communicate with the past, and as a communication process is relevant to information theory, which is thus a necessary basis of biology besides physics and chemistry. The nested genomic error-correcting codes which are needed for conserving the genetic information account for the hierarchical taxonomy which structures the living world. Moreover, the main features of biological evolution, including its trend towards increasing complexity, find an explanation within this framework. Incorporating the scientific concept of information and the science based on it in the foundations of biology can widely renew the discipline but meets epistemological difficulties which must be overcome.