The Design and Verification of Dynamic-sized Nonblocking Data Structures

<p>Modern computer systems often involve multiple processes or threads of control that communicate through shared memory. However, the implementation of correct and efficient data structures that can be shared by several processes is frequently challenging. This thesis is concerned with the design and verification of a class of shared memory algorithms known as nonblocking algorithms, which are implementations of shared data structures that provide strong progress guarantees. Nonblocking algorithms offer an appealing alternative to traditional techniques for the implementation of shared memory data structures, but they are difficult to design, and extant algorithms can often be applied in only a limited range of systems. Furthermore, because of their subtlety, it is notoriously difficult to determine whether a given nonblocking algorithm is correct. This thesis addresses these difficulties in two ways. First, we present techniques for the verification of nonblocking algorithms that dynamically allocate memory. These techniques allow the construction of formal and complete proofs of correctness, so that each proof may be checked by a mechanical proof assistant. Applying techniques first developed for the verification of distributed algorithms, we use labelled-transition systems to model algorithms and their specifications, and simulation relations to prove that an implementation meets its specification. Nonblocking algorithms often require a particular notion of simulation, called backward simulation, that is rarely necessary in other contexts. This thesis contributes to the relatively limited collective experience in the use of backward simulation. The second set of contributions addresses the limitations of many extant nonblocking algorithms. While many nonblocking algorithms allocate memory dynamically, it is difficult to determine in a nonblocking context when it is safe to free memory. We present techniques to accomplish this. Furthermore, many nonblocking algorithms depend on the availability of two powerful synchronisation primitives, known as load-linked and store-conditional, which are not normally provided by hardware. We present implementations of these primitives that work on commonly available platforms.</p>

The Design and Verification of Dynamic-sized Nonblocking Data Structures

<p>Modern computer systems often involve multiple processes or threads of control that communicate through shared memory. However, the implementation of correct and efficient data structures that can be shared by several processes is frequently challenging. This thesis is concerned with the design and verification of a class of shared memory algorithms known as nonblocking algorithms, which are implementations of shared data structures that provide strong progress guarantees. Nonblocking algorithms offer an appealing alternative to traditional techniques for the implementation of shared memory data structures, but they are difficult to design, and extant algorithms can often be applied in only a limited range of systems. Furthermore, because of their subtlety, it is notoriously difficult to determine whether a given nonblocking algorithm is correct. This thesis addresses these difficulties in two ways. First, we present techniques for the verification of nonblocking algorithms that dynamically allocate memory. These techniques allow the construction of formal and complete proofs of correctness, so that each proof may be checked by a mechanical proof assistant. Applying techniques first developed for the verification of distributed algorithms, we use labelled-transition systems to model algorithms and their specifications, and simulation relations to prove that an implementation meets its specification. Nonblocking algorithms often require a particular notion of simulation, called backward simulation, that is rarely necessary in other contexts. This thesis contributes to the relatively limited collective experience in the use of backward simulation. The second set of contributions addresses the limitations of many extant nonblocking algorithms. While many nonblocking algorithms allocate memory dynamically, it is difficult to determine in a nonblocking context when it is safe to free memory. We present techniques to accomplish this. Furthermore, many nonblocking algorithms depend on the availability of two powerful synchronisation primitives, known as load-linked and store-conditional, which are not normally provided by hardware. We present implementations of these primitives that work on commonly available platforms.</p>

Mechanical Proof of the Maxwell-Boltzmann Speed Distribution With Numerical Iterations

The Maxwell-Boltzmann speed distribution is the probability distribution that describes the speeds of the particles of ideal gases. The Maxwell-Boltzmann speed distribution is valid for both un-mixed particles (one type of particle) and mixed particles (two types of particles). For mixed particles, both types of particles follow the Maxwell-Boltzmann speed distribution. Also, the most probable speed is inversely proportional to the square root of the mass. This paper proves the Maxwell-Boltzmann speed distribution and the speed ratio of mixed particles using computer-generated data based on Newton&rsquo;s law of motion. To achieve this, this paper derives the probability density function&nbsp;&psi;^ab(u_a;v_a,v_b)&nbsp;&nbsp;of the speed u_a of the particle with mass M_a after the collision of two particles with mass M_a in speed v_a and mass M_b in speed v_b. The function&nbsp;&psi;^ab(u_a;v_a,v_b)&nbsp;&nbsp;is obtained through a unique procedure that considers (1) the randomness of the relative direction before a collision by an angle&nbsp;&alpha;. (2) the randomness of the direction after the collision by another independent angle. The function&nbsp;&psi;^ab(u_a;v_a,v_b)&nbsp;is used in the equation below for the numerical iterations to get new distributions P_new^a(u_a) from old distributions P_old^a(v_a), and repeat with P_old^a(v_a)=P_new^a(v_a), where n_a is the fraction of particles with mass M_a. &nbsp; P_new^1(u_1)=n_1 &int;_0^&infin; &int;_0^&infin; &psi;^11(u_1;v_1,v&rsquo;_1) P_old^1(v_1) P_old^1(v&rsquo;_1) dv_1 dv&rsquo;_1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; +n_2 &int;_0^&infin; &int;_0^&infin; &psi;^12(u_1;v_1,v_2) P_old^1(v_1) P_old^2(v_2) dv_1 dv_2 P_new^2(u_2)=n_1 &int;_0^&infin; &int;_0^&infin; &psi;^21(u_2;v_2,v_1) P_old^2(v_2) P_old^1(v_1) dv_2 dv_1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; +n_2 &int;_0^&infin; &int;_0^&infin; &psi;^22(u_2;v_2,v&rsquo;_2) P_old^2(v_2) P_old^2(v&rsquo;_2) dv_2 dv&rsquo;_2 The final distributions converge to the Maxwell-Boltzmann speed distributions. Moreover, the square of the root-mean-square speed from the final distribution is inversely proportional to the particle masses as predicted by Avogadro&rsquo;s law.

Mechanical Proof of the Maxwell-Boltzmann Speed Distribution With Analytical Integration

The Maxwell-Boltzmann speed distribution is the probability distribution that describes the speeds of the particles of ideal gases. The Maxwell-Boltzmann speed distribution is valid for both un-mixed particles (one type of particle) and mixed particles (two types of particles). For mixed particles, both types of particles follow the Maxwell-Boltzmann speed distribution. Also, the most probable speed is inversely proportional to the square root of the mass. The Maxwell-Boltzmann speed distribution of mixed particles is based on kinetic theory; however, it has never been derived from a mechanical point of view. This paper proves the Maxwell-Boltzmann speed distribution and the speed ratio of mixed particles based on probability analysis and Newton&rsquo;s law of motion. This paper requires the probability&nbsp;density function (PDF) &psi;^ab(u_a; v_a, v_b)&nbsp;of the speed u_a&nbsp; of the particle with mass M_a&nbsp; after the collision of two particles with mass M_a&nbsp; in speed v_a&nbsp; and mass M_b&nbsp; in speed v_b . The PDF &psi;^ab(u_a; v_a, v_b)&nbsp; in integral form has been obtained before. This paper further performs the exact integration from the integral form to obtain the PDF &psi;^ab(u_a; v_a, v_b)&nbsp; in an evaluated form, which is used in the following equation to get new distribution P_new^a(u_a)&nbsp; from old distributions P_old^a(v_a) and P_old^b(v_b). When P_old^a(v_a) and P_old^b(v_b)&nbsp; are the Maxwell-Boltzmann speed distributions, the integration P_new^a(u_a)&nbsp; obtained analytically is exactly the Maxwell-Boltzmann speed distribution. P_new^a(u_a)=&int;_0^&infin; &int;_0^&infin; &psi;^ab(u_a;v_a,v_b) P_old^a(v_a) P_old^b(v_b) dv_a dv_b,&nbsp;&nbsp; &nbsp;a,b = 1 or 2 The mechanical proof of the Maxwell-Boltzmann speed distribution presented in this paper reveals the unsolved mechanical mystery of the Maxwell-Boltzmann speed distribution since it was proposed by Maxwell in 1860. Also, since the validation is carried out in an analytical approach, it proves that there is no theoretical limitation of mass ratio to the Maxwell-Boltzmann speed distribution. This provides a foundation and methodology for analyzing the interaction between particles with an extreme mass ratio, such as gases and neutrinos.

Mechanical Proof of the Maxwell Speed Distribution

This article derives the probability density function &psi;&xi;;x,x&#39; &nbsp;of the resulting speed &xi; &nbsp;from the collision of two particles with speeds x &nbsp;and x&#39; . This function had been left unsolved for about 150 years. Then uses two approaches to obtain the Maxwell speed distribution: (1) Numerical iteration: using the equation Pnew&xi;=0&infin;0&infin;&psi;&xi;;x,x&#39; ∙Poldx∙Poldx&#39; dxdx&#39; &nbsp; to get the new speed distribution from the old speed distribution. Also, after 9 iterations, the distribution converges to the Maxwell speed distribution. (2) Analytical integration: using the Maxwell speed distribution as the Poldx , and then getting Pnew&xi; &nbsp;from the above integration. The result of Pnew&xi; &nbsp;from analytical integration is proved to be exactly the Maxwell speed distribution.

An actuated neural probe architecture for reducing gliosis-induced recording degradation

Glial encapsulation of chronically implanted neural probes inhibits recording and stimulation, and this signal loss is a significant factor limiting the clinical viability of most neural implant topologies for decades-long implantation. We demonstrate a mechanical proof of concept for silicon shank-style neural probes intended to minimize gliosis near the recording sites. Compliant whiskers on the edges of the probe fold inward to minimize tissue damage during insertion. Once implanted to the target depth and retracted slightly, these whiskers splay outward. The splayed tips, on which recording sites could be patterned, extend beyond the typical 50-100 micron radius of a glial scar. The whiskers are micron-scale to minimize or avoid glial scarring. Electrically inactive devices with whiskers of varying widths and curvature were designed and monolithically fabricated from a five-micron silicon-on-insulator (SOI) wafer, and their mechanical functionality was demonstrated in a 0.6% agar brain phantom. Deflection was plotted versus deflection speed, and those that were most compliant actuated successfully. This probe requires no preparation for use beyond what is typical for a shank-style silicon probe.