Grounds for Trust: Essential Epistemic Opacity and Computational Reliabilism

Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations (Parker in Synthese 169(3):483–496, 2009; Morrison in Philos Stud 143(1):33–57, 2009), the nature of computer data (Barberousse and Vorms, in: Durán, Arnold (eds) Computer simulations and the changing face of scientific experimentation, Cambridge Scholars Publishing, Barcelona, 2013; Humphreys, in: Durán, Arnold (eds) Computer simulations and the changing face of scientific experimentation, Cambridge Scholars Publishing, Barcelona, 2013), and the explanatory power of computer simulations (Krohs in Int Stud Philos Sci 22(3):277–292, 2008; Durán in Int Stud Philos Sci 31(1):27–45, 2017). The aim of this article is to show that these authors are right in assuming that results of computer simulations are to be trusted when computer simulations are reliable processes. After a short reconstruction of the problem of epistemic opacity, the article elaborates extensively on computational reliabilism, a specified form of process reliabilism with computer simulations located at the center. The article ends with a discussion of four sources for computational reliabilism, namely, verification and validation, robustness analysis for computer simulations, a history of (un)successful implementations, and the role of expert knowledge in simulations.     

Modeling and Simulation of Laser Processing of Particulate-Functionalized Materials

The objective of this paper is to focus on one of the “building blocks” of additive manufacturing technologies, namely selective laser-processing of particle-functionalized materials. Following a series of work in Zohdi (Int J Numer Methods Eng 53:1511–1532, 2002; Philos Trans R Soc Math Phys Eng Sci 361(1806):1021–1043, 2003; Comput Methods Appl Mech Eng 193(6–8):679–699, 2004; Comput Methods Appl Mech Eng 196:3927–3950, 2007; Int J Numer Methods Eng 76:1250–1279, 2008; Comput Methods Appl Mech Eng 199:79–101, 2010; Arch Comput Methods Eng 1–17. doi: 10.1007/s11831-013-9092-6, 2013; Comput Mech Eng Sci 98(3):261–277, 2014; Comput Mech 54:171–191, 2014; J Manuf Sci Eng ASME doi: 10.1115/1.4029327, 2015; CIRP J Manuf Sci Technol 10:77–83, 2015; Comput Mech 56:613–630, 2015; Introduction to computational micromechanics. Springer, Berlin, 2008; Introduction to the modeling and simulation of particulate flows. SIAM (Society for Industrial and Applied Mathematics), Philadelphia, 2007; Electromagnetic properties of multiphase dielectrics: a primer on modeling, theory and computation. Springer, Berlin, 2012), a laser-penetration model, in conjunction with a Finite Difference Time Domain Method using an immersed microstructure method, is developed. Because optical, thermal and mechanical multifield coupling is present, a recursive, staggered, temporally-adaptive scheme is developed to resolve the internal microstructural fields. The time step adaptation allows the numerical scheme to iteratively resolve the changing physical fields by refining the time-steps during phases of the process when the system is undergoing large changes on a relatively small time-scale and can also enlarge the time-steps when the processes are relatively slow. The spatial discretization grids are uniform and dense enough to capture fine-scale changes in the fields. The microstructure is embedded into the spatial discretization and the regular grid allows one to generate a matrix-free iterative formulation which is amenable to rapid computation, with minimal memory requirements, making it ideal for laptop computation. Numerical examples are provided to illustrate the modeling and simulation approach, which by design, is straightforward to computationally implement, in order to be easily utilized by researchers in the field. More advanced conduction models, based on thermal-relaxation, which are a key feature of fast-pulsing laser technologies, are also discussed.     

Mesh generation for confined fusion plasma simulation

XGC1 and M3D-C ¹ are two fusion plasma simulation codes being developed at Princeton Plasma Physics Laboratory. XGC1 uses the particle-in-cell method to simulate gyrokinetic neoclassical physics and turbulence (Chang et al. Phys Plasmas 16(5):056108, 2009; Ku et al. Nucl Fusion 49:115021, 2009; Admas et al. J Phys 180(1):012036, 2009). M3D-\(C^1\) solves the two-fluid resistive magnetohydrodynamic equations with the \(C^1\) finite elements (Jardin J comput phys 200(1):133–152, 2004; Jardin et al. J comput Phys 226(2):2146–2174, 2007; Ferraro and Jardin J comput Phys 228(20):7742–7770, 2009; Jardin J comput Phys 231(3):832–838, 2012; Jardin et al. Comput Sci Discov 5(1):014002, 2012; Ferraro et al. Sci Discov Adv Comput, 2012; Ferraro et al. International sherwood fusion theory conference, 2014). This paper presents the software tools and libraries that were combined to form the geometry and automatic meshing procedures for these codes. Specific consideration has been given to satisfy the mesh configuration and element shape quality constraints of XGC1 and M3D-\(C^1\).     

Superconvergent Two-Grid Methods for Elliptic Eigenvalue Problems

Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm (Xu and Zhou in Math Comput 70(233):17–25, 2001), the two-space method (Racheva and Andreev in Comput Methods Appl Math 2:171–185, 2002), the shifted inverse power method (Hu and Cheng in Math Comput 80:1287–1301, 2011; Yang and Bi in SIAM J Numer Anal 49:1602–1624, 2011), and the polynomial preserving recovery enhancing technique (Naga et al. in SIAM J Sci Comput 28:1289–1300, 2006). Our new algorithms compare favorably with some existing methods and enjoy superconvergence property.     

Direct Discontinuous Galerkin Method and Its Variations for Second Order Elliptic Equations

In this paper, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under \(L^2\) norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Math 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal \((k+1)\)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal \((k+1)\)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.     

The computational capability of chemical reaction automata

We propose a new computing model called chemical reaction automata (CRAs) as a simplified variant of reaction automata (RAs) studied in recent literature (Okubo in RAIRO Theor Inform Appl 48:23–38 2014; Okubo et al. in Theor Comput Sci 429:247–257 2012a, Theor Comput Sci 454:206–221 2012b). We show that CRAs in maximally parallel manner are computationally equivalent to Turing machines, while the computational power of CRAs in sequential manner coincides with that of the class of Petri nets, which is in marked contrast to the result that RAs (in both maximally parallel and sequential manners) have the computing power of Turing universality (Okubo 2014; Okubo et al. 2012a). Intuitively, CRAs are defined as RAs without inhibitor functioning in each reaction, providing an offline model of computing by chemical reaction networks (CRNs). Thus, the main results in this paper not only strengthen the previous result on Turing computability of RAs but also clarify the computing powers of inhibitors in RA computation.     

On Optimally Partitioning a Text to Improve Its Compression

In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once. This problem was introduced in Buchsbaum et al. (Proc. of 11th ACM-SIAM Symposium on Discrete Algorithms, pp. 175–184, 2000; J. ACM 50(6):825–851, 2003) in the context of table compression, and then further elaborated and extended to strings and trees by Ferragina et al. (J. ACM 52:688–713, 2005; Proc. of 46th IEEE Symposium on Foundations of Computer Science, pp. 184–193, 2005) and Mäkinen and Navarro (Proc. of 14th Symposium on String Processing and Information Retrieval, pp. 229–241, 2007). Unfortunately, the literature offers poor solutions: namely, we know either a cubic-time algorithm for computing the optimal partition based on dynamic programming (Buchsbaum et al. in J. ACM 50(6):825–851, 2003; Giancarlo and Sciortino in Proc. of 14th Symposium on Combinatorial Pattern Matching, pp. 129–143, 2003), or few heuristics that do not guarantee any bounds on the efficacy of their computed partition (Buchsbaum et al. in Proc. of 11th ACM-SIAM Symposium on Discrete Algorithms, pp. 175–184, 2000; J. ACM 50(6):825–851, 2003), or algorithms that are efficient but work in some specific scenarios (such as the Burrows-Wheeler Transform, see e.g. Ferragina et al. in J. ACM 52:688–713, 2005; Mäkinen and Navarro in Proc. of 14th Symposium on String Processing and Information Retrieval, pp. 229–241, 2007) and achieve compression performance that might be worse than the optimal-partitioning by a Ω(log?n/log?log?n) factor. Therefore, computing efficiently the optimal solution is still open (Buchsbaum and Giancarlo in Encyclopedia of Algorithms, pp. 939–942, 2008). In this paper we provide the first algorithm which computes in O(nlog?_1+ε n) time and O(n) space, a partition of T whose compressed output is guaranteed to be no more than (1+ε)-worse the optimal one, where ε may be any positive constant fixed in advance. This result holds for any base-compressor C whose compression performance can be bounded in terms of the zero-th or the k-th order empirical entropy of the text T. We will also discuss extensions of our results to BWT-based compressors and to the compression booster of Ferragina et al. (J. ACM 52:688–713, 2005).     

<Emphasis Type="Italic">δ</Emphasis>-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

Intuitionistic fuzzy set is capable of handling uncertainty with counterpart falsities which exist in nature. Proximity measure is a convenient way to demonstrate impractical significance of values of memberships in the intuitionistic fuzzy set. However, the related works of Pappis (Fuzzy Sets Syst 39(1):111–115, 1991), Hong and Hwang (Fuzzy Sets Syst 66(3):383–386, 1994), Virant (2000) and Cai (IEEE Trans Fuzzy Syst 9(5):738–750, 2001) did not model the measure in the context of the intuitionistic fuzzy set but in the Zadeh’s fuzzy set instead. In this paper, we examine this problem and propose new notions of δ-equalities for the intuitionistic fuzzy set and δ-equalities for intuitionistic fuzzy relations. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ. The applications of δ-equalities are important to fuzzy statistics and fuzzy reasoning. Several characteristics of δ-equalities that were not discussed in the previous works are also investigated. We apply the δ-equalities to the application of medical diagnosis to investigate a patient’s diseases from symptoms. The idea is using δ-equalities for intuitionistic fuzzy relations to find groups of intuitionistic fuzzified set with certain equality or similar degrees then combining them. Numerical examples are given to illustrate validity of the proposed algorithm. Further, we conduct experiments on real medical datasets to check the efficiency and applicability on real-world problems. The results obtained are also better in comparison with 10 existing diagnosis methods namely De et al. (Fuzzy Sets Syst 117:209–213, 2001), Samuel and Balamurugan (Appl Math Sci 6(35):1741–1746, 2012), Szmidt and Kacprzyk (2004), Zhang et al. (Procedia Eng 29:4336–4342, 2012), Hung and Yang (Pattern Recogn Lett 25:1603–1611, 2004), Wang and Xin (Pattern Recogn Lett 26:2063–2069, 2005), Vlachos and Sergiadis (Pattern Recogn Lett 28(2):197–206, 2007), Zhang and Jiang (Inf Sci 178(6):4184–4191, 2008), Maheshwari and Srivastava (J Appl Anal Comput 6(3):772–789, 2016) and Support Vector Machine (SVM).     

WSGD-OSC Scheme for Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation

In this paper, a new numerical approximation is discussed for the two-dimensional distributed-order time fractional reaction–diffusion equation. Combining with the idea of weighted and shifted Grünwald difference (WSGD) approximation (Tian et al. in Math Comput 84:1703–1727, 2015; Wang and Vong in J Comput Phys 277:1–15, 2014) in time, we establish orthogonal spline collocation (OSC) method in space. A detailed analysis shows that the proposed scheme is unconditionally stable and convergent with the convergence order \(\mathscr {O}(\tau ^2+\Delta \alpha ^2+h^{r+1})\), where \(\tau , \Delta \alpha , h\) and r are, respectively the time step size, step size in distributed-order variable, space step size, and polynomial degree of space. Interestingly, we prove that the proposed WSGD-OSC scheme converges with the second-order in time, where OSC schemes proposed previously (Fairweather et al. in J Sci Comput 65:1217–1239, 2015; Yang et al. in J Comput Phys 256:824–837, 2014) can at most achieve temporal accuracy of order which depends on the order of fractional derivatives in the equations and is usually less than two. Some numerical results are also given to confirm our theoretical prediction.     

SAW based phononic crystal sensor,technological challenges and solutions

Phononic crystals (PnC) with a specifically designed liquid-filled defect have been recently introduced as a novel sensor platform (Lucklum et al. in Sens Actuators B Chem 171–172:271–277, 2012). Sensors based on this principle feature a band gap covering the typical input span of the measurand as well as a narrow transmission peak within the band gap where the frequency of maximum transmission is governed by the measurand. This approach has been applied for determination of volumetric properties of liquids (Lucklum et al. in Sens Actuators B Chem 171–172:271–277, 2012; Oseev et al. in Sens Actuators B Chem 189:208–212, 2013; Lucklum and Li in Meas Sci Technol 20(12):124014, 2009) and has demonstrated attractive sensitivity. One way to improve sensitivity requires higher probing frequencies in the range of 100 MHz and above. In this range surface acoustic wave (SAW) devices are an established basis for sensors. We have performed first tests towards a PnC microsensors (Lucklum et al. in Towards a SAW based phononic crystal sensor platform. In: 2013 Joint European frequency and time forum and international frequency control symposium (EFTF/IFC), pp 69–72, 2013). The respective feature size of the PnC SAW sensor has dimensions in the range of 10 µm and below. Whereas those dimensions are state of the art for common MEMS materials, etching of holes and cavities in piezoelectric materials that have an aspect ratio diameter/depth is still challenging. In this contribution we describe an improved technological process able to realize considerably deep and uniform holes in a SAW substrate.     

The Limits to Credit Growth: Mitigation Policies and Macroprudential Regulations to Foster Macrofinancial Stability and Sustainable Debt

In this paper we study an economy with a high degree of financialization in which (non-financial) firms need loans from commercial banks to finance production, service debt, and make long-term investments. Along the business cycle, the economy follows a Minsky base cycle with firms traversing through the various stages of financial fragility, i.e. hedge, speculative and Ponzi finance (cf., Minsky in The financial instability hypothesis: a restatement. Hyman P Minsky archive paper, vol 180, pp 541–552, 1978; Stabilizing an unstable economy. Yale University Press, 2nd edn 2008, McGraw-Hill, New York, 1986; The financial instability hypothesis. Economics working paper archive wp74. The Jerome Levy Economics Institute of Bard College, 1992). In the speculative financial stage cash flows are insufficient to finance the repayment of principle but sufficient for paying interest, so banks are willing to roll-over credits in order to prevent loan defaults. In the Ponzi financial position even interest payments cannot be served, but banks my still be willing to keep firms alive through “extend and pretend” loans, also known as zombie-lending (Caballero et al. in Am Econ Rev 98(5):1943–1977, 2008). This lending behavior may cause credit bubbles with increasing leverage ratios. Empirical evidence suggests that recessions following such leveraging booms are more severe and can be associated to higher economic costs (Jordà et al. in J Money Credit Bank 45(s2):3–28, 2013; Schularick and Taylor in Am Econ Rev 102(2):1029–1061, 2012). We study macroprudential regulations aimed at: (i) the prevention and mitigation of credit bubbles, (ii) ensuring macro-financial stability, and (iii) limiting the ability of banks to create unsustainable debt bubbles. Our results show that limiting the credit growth by using a non-risk-weighted capital ratio has slightly positive effects, while using loan eligibility criteria such as cutting off funding to all financially unsound firms (speculative and Ponzi) has strong positive effects.     

Virtual Machines and Real Implementations

What does it take to implement a computer? Answers to this question have often focused on what it takes for a physical system to implement an abstract machine. As Joslin (Minds Mach 16:29–41, 2006) observes, this approach neglects cases of software implementation—cases where one machine implements another by running a program. These cases, Joslin argues, highlight serious problems for mapping accounts of computer implementation—accounts that require a mapping between elements of a physical system and elements of an abstract machine. The source of these problems is the complexity introduced by common design features of ordinary computers, features that would be relevant to any real-world software implementation (e.g., virtual memory). While Joslin is focused on contemporary views, his discussion also suggests a counterexample to recent mapping accounts which hold that genuine implementation requires simple mappings (Millhouse in Br J Philos Sci, 2017.  https://doi.org/10.1093/bjps/axx046; Wallace in The emergent multiverse, Oxford University Press, Oxford, 2014). In this paper, I begin by clarifying the nature of software implementation and disentangling it from closely related phenomena like emulation and simulation. Next, I argue that Joslin overstates the degree of complexity involved in his target cases and that these cases may actually give us reasons to favor simplicity-based criteria over relevant alternatives. Finally, I propose a novel problem for simplicity-based criteria and suggest a tentative solution.     

A secure and efficient payment protocol based on ElGamal cryptographic algorithms

In this paper we present a secure and efficient transaction protocol that provides the anonymity and can detect the double spending. The proposed payment system is based on the ElGamal encryption scheme, the ElGamal signature scheme and the ElGamal blind signature protocol. We show that our transaction protocol is secure and efficient. We give the definitions of unlinkability and unforgeability of our security model and we prove that the proposed transaction protocol is unforgeable and satisfies the unlinkability property. We show that the proposed system is more efficient, in terms of the computation and communication cost, than the compared payment systems (Eslami et al. in Electron Commer Res Appl 10:59–66, 2011; Chen et al. in Electron Commer Res Appl 10:279–287, 2011; Liu et al. in Proceedings of second European PKI workshop: research and applications. Lecture notes in computer science, vol 3545, pp 206–214, 2005 and Chen et al. in Electron Commer Res Appl 10:673–682, 2011) for a customer who withdraws and spends an e-coin and for the merchant who verifies an electronic coin. Also, the proposed e-cash system is useful for the electronic transactions when the connection between the bank and the merchant is not available during the payment protocol. This means a less bandwidth of the payment protocol and then increases the speed of the electronic transaction.     

Two axiomatic characterizations for the system of spheres-based (and the Epistemic Entrenchment-based) multiple contractions

In some recent works (Reis 2011, Fermé and Reis, J. Philos. Log. 41, 29–52, 2012, Fermé and Reis, Rev. Symb. Log. 6, 460–487, 2013) two new kinds of multiple contraction functions have been proposed, namely the system of spheres-based multiple contractions and the epistemic entrenchment-based multiple contractions, as generalizations (to the case of multiple contraction) of the well-known classes of systems of spheres-based and of epistemic entrenchment-based (singleton) contractions. Additionally, a representation theorem for the class of epistemic entrenchment-based multiple contraction has been proposed, and it has been shown that the two newly proposed constructions are equivalent, in the sense that a multiple contraction function is a system of spheres-based multiple contraction if and only if it is an epistemic entrenchment-based multiple contraction. In this paper we present two axiomatic characterizations for those multiple contraction functions which differ from the one mentioned above and, in particular, make use of some more intuitive postulates.     

Information Lower Bounds via Self-Reducibility

We use self-reduction methods to prove strong information lower bounds on two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product (IP). In our first result we affirm the conjecture that the information cost of GHD is linear even under the uniform distribution, which strengthens the Ω(n) bound recently shown by Kerenidis et al. (2012), and answers an open problem from Chakrabarti et al. (2012). In our second result we prove that the information cost of IP_n is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the Ω(n) lower bound recently proved by Braverman and Weinstein (Electronic Colloquium on Computational Complexity (ECCC) 18, 164 2011). Our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past (Chakrabarti et al. 2001; Bar-Yossef et al. J. Comput. Syst. Sci. 68(4), 702–732 2004; Barak et al. 2010) used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner.     

Worlds,Events, and Inertia

The semantics of progressive sentences presents a challenge to linguists and philosophers alike. According to a widely accepted view, the truth-conditions of progressive sentences rely essentially on a notion of inertia. Dowty (Word meaning and Montague grammar: the semantics of verbs and times in generative grammar and in Montague’s PTQ, D. Reidel Publishing Company, Dordrecht, 1979) suggested inertia worlds to implement this “inertia idea” in a formal semantic theory of the progressive. The main thesis of the paper is that the notion of inertia went through a subtle, but crucial change when worlds were replaced by events in Landman (Nat Lang Semant 1:1–32, 1992) and Portner (Language 74(4):760–787, 1998), and that this new, event-related concept of inertia results in a possibility-based theory of the progressive. An important case in point in the paper is a proof that, despite its surface structure, the theory presented in Portner (1998) does not implement the notion of inertia in Dowty (1979); rather, it belongs together with Dowty’s earlier, 1977 theory according to which the progressive is a possibility operator.     

Unifying Conceptual Spaces: Concept Formation in Musical Creative Systems

We examine Gärdenfors’ theory of conceptual spaces, a geometrical form of knowledge representation (Conceptual spaces: The geometry of thought, MIT Press, Cambridge, 2000), in the context of the general Creative Systems Framework introduced by Wiggins (J Knowl Based Syst 19(7):449–458, 2006a; New Generation Comput 24(3):209–222, 2006b). Gärdenfors’ theory offers a way of bridging the traditional divide between symbolic and sub-symbolic representations, as well as the gap between representational formalism and meaning as perceived by human minds. We discuss how both these qualities may be advantageous from the point of view of artificial creative systems. We take music as our example domain, and discuss how a range of musical qualities may be instantiated as conceptual spaces, and present a detailed conceptual space formalisation of musical metre.     

Connectivity Preserving Multivalued Functions in Digital Topology

We study connectivity preserving multivalued functions (Kovalevsky in A new concept for digital geometry, shape in picture, 1994) between digital images. This notion generalizes that of continuous multivalued functions (Escribano et al. in Discrete geometry for computer imagery, lecture notes in computer science, 2008; Escribano et al. in J Math Imaging Vis 42:76–91, 2012) studied mostly in the setting of the digital plane \({\mathbb {Z}}^2\). We show that connectivity preserving multivalued functions, like continuous multivalued functions, are appropriate models for digital morphological operations. Connectivity preservation, unlike continuity, is preserved by compositions, and generalizes easily to higher dimensions and arbitrary adjacency relations.