*τt*1<*t*2 *Qnp*,*j* − *t*0 → 0,

*where:*

$$t\_0 = \begin{cases} 0 & \text{if } j < -1 \\ \omega\_n c\_{\frac{\pi}{2}} & \text{if } j = -1, \end{cases} \tag{105}$$

*for all n* ∈ N.

> *Under the same hypothesis, if j* > −1 *in* Z, *then:*

$$\left| \left. \pi\_{t\_1 < t\_2} \left( Q\_{p,j}^n \right) \right| \right| \to \infty,\tag{106}$$

*for all n* ∈ N.

**Proof.** The estimations (105) and (106), for suitably big *t*1 ∈ R, are obtained by (103).

### **10. Semicircularity of Certain Free Sums in** LS*t*1<*t*2

As in Section 9, we will let LS be the Banach ∗-subalgebra (72) of the free Adelic filtration LS, and let LS0 be the semicircular filtration (LS, *τ*0) of (80).

Let (*A*, *ϕ*) be an arbitrary topological ∗-probability space and *a* ∈ (*A*, *ϕ*). We say a free random variable *a* is a *free sum* in (*A*, *ϕ*), if:

$$a = \sum\_{l=1}^{N} \mathbf{x}\_l,\text{ with } \mathbf{x}\_l \in (A, \,\,\phi)\_l$$

 and the summands *x*1, ..., *xN* of *a* are free from each other in (*A*, *ϕ*), for *N* ∈ N \ {1}.

Let *t*1 < *t*2 be suitable in R in the sense of **NA 9.2**, and let LS*t*1<*t*2 be the corresponding semicircular [*t*1, *t*2]-filtration. Now, we define free random variables *X* and *Y* of LS,

$$X = \sum\_{l=1}^{N} \mathbb{Q}\_{p\_l, \dot{\jmath}\_l}^{\eta\_l} and Y = \sum\_{l=1}^{N} \mathbb{G}\_{p\_l, \dot{\jmath}\_l}^{\eta\_l} \tag{107}$$

for *Qpl*,*jl* ∈ Q and Θ*pl*,*jl* ∈ Θ, for all *l* = 1, ..., *N*, for *N* ∈ N \ {1}.

Remark that, the operator *X* (or *Y*) of (107) is a free sum in LS, if and only if the summands *Qnl pl*,*jl* (resp., Θ*nl pl*,*jl*), which are the free reduced words with their lengths one, are free from each other in LS, if and only if *Qpl*,*jl* (resp., Θ*pl*,*jl*) are contained in the mutually-distinct free blocks C[{*Qpl*,*jl* }] of LS by (74), if and only if the pairs (*pl*, *jl*) are mutually distinct from each other in the Cartesian product P × Z, for all *l* = 1, ..., *N*. i.e., the given operators *X* and *Y* of (107) are free sums in LS, if and only if:

$$<\langle p\_{l\_1}, j\_{l\_1} \rangle \neq (p\_{l\_2}, j\_{l\_2}) \text{in} \mathcal{P} \times \mathbb{Z}\_\star \tag{108}$$

for all *l*1 = *l*2 in {1, ..., *N*}.

**Lemma 4.** *Let X and Y be in the sense of* (107) *in the semicircular filtration* LS0. *Assume that the pairs* (*pl*, *jl*) *are mutually distinct from each other in* P × Z, *for all l* = 1, *..., N*, *for N* ∈ N \ {1}. *Then:*

$$
\pi^0(X) = \sum\_{l=1}^N \left(\omega\_{n\_l} p\_l^{2(j\_l+1)} c\_{\frac{n\_l}{2}}\right),
$$

$$
\pi^0(Y) = \sum\_{l=1}^N \left(\omega\_{n\_l} c\_{\frac{n\_l}{2}}\right).
\tag{109}
$$

*and:*

\*\*Proof.\*\* Let  $\mathbb{X}$  and  $\mathbb{Y}$  be given as above in  $\mathbb{L}\mathbb{S}\_{0}$ . By the assumption that the pairs  $(p\_{\ell}, j\_{\ell})$  are mutually distinct from each other in  $\mathcal{P} \times \mathbb{Z}$ , these operators  $X$  and  $Y$  satisfy the condition (108); equivalently, they are free sums in  $\mathbb{L}\mathbb{S}\_{0}$ .

Therefore, one has that:

$$\begin{aligned} \tau^0(X) &= \sum\_{l=1}^N \tau^0 \left( Q^{n\_l}\_{p\_l, j\_l} \right) = \Sigma^N\_{l=1} \, \tau^0\_{p\_l, j\_l} \left( Q^{n\_l}\_{p\_l, j\_l} \right), \\ &= \Sigma^N\_{l=1} \left( \omega\_{n\_l} p\_l^{2(j\_l+1)} c\_{\frac{n\_l}{2}} \right). \end{aligned}$$

by the *p*2(*jl*+1) *l* -semicircularity of *Qpl*,*jl* ∈ Q, for all *l* = 1, ..., *N*.

Similarly, one can get that:

$$
\pi^0(\mathcal{Y}) = \Sigma\_{l=1}^N \pi\_{p\_l, j\_l}^0 \left( \Theta\_{p\_l, j\_l}^{n\_l} \right) = \Sigma\_{l=1}^N \left( \omega\_{n\_l} c\_{\frac{n\_l}{2}} \right),
$$

by the semicircularity of Θ*pl*,*jl* ∈ Θ, for all *l* = 1, ..., *N*.

Now, for the operators *X* and *Y* of (107), we consider how our truncation distorts the free-distributional data (109).

For a given closed interval [*t*1, *t*2] in R, where *t*1 < *t*2 are suitable in R, we define:

$$\mathcal{P}\_{[t\_1, t\_2]} = \{ p \in \mathcal{P} : t\_1 \le p \le t\_2 \} = \mathcal{P} \cap [t\_1, t\_2]\_{\mathcal{I}}$$

and:

$$\mathcal{P}\_{[t\_1, t\_2]}^{\varepsilon} = \mathcal{P} \backslash \mathcal{P}\_{[t\_1, t\_2]} \tag{110}$$

in P.

By (110), the family {P[*t*1,*t*2], P*c*[*t*1,*t*2]} forms a partition of the set P of all primes for the fixed interval [*t*1, *t*2]. Of course, if *t*1 < *t*2 are not suitable, then:

$$\mathcal{P}\_{[t\_1, t\_2]} = \mathcal{Q}\_{\prime} \text{ and hence, } \mathcal{P} = \mathcal{P}\_{[t\_1, t\_2]}^{\varepsilon}.$$

**Theorem 10.** *Let X and Y be the operators* (107)*, and assume they are free sums in the semicircular filtration* LS0; *and let* LS*t*1<*t*2*be the semicircular* [*t*1, *t*2]*-filtration for suitable t*1 < *t*2 *in* R*. Then:*

$$\pi\_{t\_1 < t\_2}(X) = \sum\_{p\_I \in \mathcal{P}\_{[t\_1, t\_2] : (p\_1, \dots, p\_N)}} \left( \omega\_{\mathcal{W}\_I} p\_I^{2(j\_l + 1)} \mathfrak{c}\_{\frac{n}{2}} \right),$$

*and:*

$$\pi\_{t\_1 < t\_2}(Y) = \sum\_{p\_l \in \mathcal{P}\_{[t\_1 < t\_2] : (p\_1, \dots, p\_N)}} \left( \omega\_{n\_l} c\_{\frac{n\_l}{2}} \right), \tag{111}$$

*where:*

$$\mathcal{P}\_{[t\_1, t\_2]:(p\_1, \dots, p\_N)} = \mathcal{P}\_{[t\_1, t\_2]} \cap \{p\_1, \dots, p\_N\} \text{ in } \mathcal{P}\_{\prime}$$

*where* P[*t*1,*t*2] *is in the sense of* (110) *in* P. *Clearly, if* P[*t*1,*t*2]:(*p*1,...,*pN*) *is empty in* P, *then the formulas in* (111) *vanish.*

**Proof.** The proof of (111) is done by (95), (96), (98), and (109). Indeed, if:

$$\mathcal{P}\_{[t\_1, t\_2]:(p\_1, \dots, p\_N)} = \mathcal{P}\_{[t\_1, t\_2]} \cap \{p\_1, \dots, p\_N\} \text{ in } \mathcal{P}\_{\prime}$$

where P[*t*1,*t*2] is in the sense of (110), and if:

$$\mathcal{P}\_{[t\_1, t\_2]:(p\_1, \dots, p\_N)} \neq \mathcal{Q}\_{\prime \prime}$$

then:

$$\pi\_{t\_1 < t\_2}(X) = \sum\_{p\_l \in \mathcal{P}\_{[t\_1, t\_2] \colon (p\_1, \dots, p\_N)}} \pi\_{p\_l, j\_l}^0 \left( Q\_{p\_l, j\_l}^{n\_l} \right),$$

by (98)

$$=\sum\_{p\_l \in \mathcal{P}\_{[\mathfrak{l}\_1, \mathfrak{l}\_2] : (\mathcal{P}\_1, \dots, \mathcal{P}\_N)}} \left(\omega\_{n\_l} p\_l^{2(j\_l+1)} c\_{\frac{n\_l}{2}}\right) \dots$$

by the *p*2(*j*+1)-semicircularity of *Qp*,*j* ∈ Q.

> Similarly, one can get that:

$$\pi\_{t\_1 < t\_2}(\mathcal{Y}) = \sum\_{p\_l \in \mathcal{P}\_{[t\_1, t\_2] : (\mathcal{P}\_1, \dots, \mathcal{P}N)}} \left( \omega\_{n\_l} c\_{\#} \right) \cdot \zeta$$

by the semicircularity of Θ*p*,*j* ∈ Θ. Therefore, the free-distributional data (111) holds, whenever:

$$\mathcal{P}\_{[t\_1, t\_2]:(p\_1, \dots, p\_N)} \neq \mathcal{Q} \text{ in } \mathcal{P}.$$

Definitely, if:

$$\mathcal{P}\_{[t\_1, t\_2]:(p\_1, \dots, p\_N)} = \mathcal{Q}\_{\prime}$$

then:

$$
\pi\_{t\_1 < t\_2}(X) = O(X) = 0 = O(Y) = \pi\_{t\_1 < t\_2}(Y).
$$

Therefore, the truncated free-distributional data (111) hold.

**Remark 4.** *Let us compare the free-distributional data* (109) *and* (111)*. One can check the differences between them dictated by the choices of* [*t*1, *t*2] *in* R. *Thus, the formula* (111) *also illustrates how our truncations on* P *distort the original free-probabilistic information on the semicircular filtration* LS0*.*

Let *q*0 be a fixed prime in P. Choose *t*0 < *s*0 ∈ R such that: (i) these quantities *t*0 and *s*0 satisfy:

$$t\_0 \le q\_0 \le s\_0 \text{ in } \mathbb{R}\_\prime$$

and (ii) *q*0 is the only prime in the closed interval [*t*0, *s*0] in R.

By the *Archimedean property* on R (or *the axiom of choice*), the existence of such interval [*t*0, *s*0], satisfying (i) and (ii) for the fixed prime *q*0, is guaranteed; however, the choices of the quantities *t*0 < *s*0 are of course not unique.

**Definition 18.** *Let q*0 ∈ P, *and let t* < *s* ∈ R *be the real numbers satisfying the conditions (i) and (ii) of the above paragraph. Then, the suitable closed interval* [*t*, *s*] *is called a q*0*-neighborhood.*

Depending on prime-neighborhoods, one can obtain the following semicircularity condition on our semicircular truncated-filtrations.

**Corollary 5.** *Let p* ∈ P, [*t*, *s*] *be a p-neighborhood in* R, *and* LS*t*<*s be the corresponding semicircular* [*t*, *s*]*-filtration. If X and Y are free sums formed by* (107) *in the semicircular filtration* LS0, *then:*

$$
\pi\_{l

$$
\pi\_{l$$
$$

*where δ is the Kronecker delta.*

*and:*

**Proof.** The free-distributional data (112) are a special case of (111), under the prime-neighborhood condition. Indeed, in this case,

$$\mathcal{P}\_{[t,s]:(p\_1,\ldots,p\_N)} = \{p\} \cap \{p\_1,\ldots,p\_N\} = \left\{\begin{array}{l} \{p\} \quad \text{or} \\ \mathcal{Q}\_{\prime} \end{array}\right\}$$

where P[*t*,*s*]:(*p*1,...,*pN*) is in the sense of (111).

More general to (112), we obtain the following result.

**Proposition 10.** *Let p* ∈ P *and* [*t*, *s*] *be a p-neighborhood in* R, *and let* LS*t*<*s be the corresponding semicircular* [*t*, *s*]*-filtration. Then, a free random variable T* ∈ LS*t*<*s has its non-zero free distribution, if and only if there exists a non-zero summand T*0 *of T*, *such that:*

$$T\_0 \in \mathbb{L} \mathbb{S}\_p \\ \|f\|\_{\ell^\infty(\mathbb{S}^\*)} \tag{113}$$

*where* LS*p* = *j*∈ZC[{Θ*p*,*j*}] *is a Banach* ∗*-subalgebra* (82) *of* LS. **Proof.** By (98), if *T* ∈ LS*t*<*s* has its non-zero free distribution, then there exists a non-zero summand *T*0 of *T* which can be a linear combination of free reduced words contained in - *t*≤*q*≤*s*in P LS*q*, and hence,

$$T0 \in \mathop{\mathbb{K}\_{t \le p}}\_{t \le q} \mathop{\star}\_{\le s} \mathbb{L} \mathcal{B}\_{q\_{\prime}} \tag{114}$$

where LS*q* are in the sense of (82), for *q* ∈ P.

> Since [*t*, *s*] is a *p*-neighborhood, the relation (114) is equivalent to:

$$T\_0 \in \mathbb{L} \mathbb{S}\_p. \tag{115}$$

Clearly, the converse holds true as well, by (98).

Therefore, a free random variable *T* ∈ LS*t*<*s* has its non-zero free distribution, if and only if *T* contains its non-zero summand *T*0 ∈ LS*p*, by (115); equivalently, the statement (113) holds true.

By (112) and (113), we obtain the following interesting result.

**Theorem 11.** *Let X*1 = ∑*Nl*=1 *Qpl*,*jl and Y*1 = ∑*Nl*=1 Θ*pl*,*jl be in the sense of* (107) *in the semicircular filtration* LS0, *and assume that* (*pl*, *jl*) *are mutually distinct in* P × Z, *for l* = 1, *..., N*, *for N* ∈ N \ {1}. *Suppose we fix:*

$$p\_{l\_0} \in \{p\_{1\prime}, \dots, p\_N\}\_{\prime}$$

*and take a pl*0*-neighborhood* [*t*0, *s*0] *in* R. *Then:*

$$X\_1
is\_{l\_0}^{2(j\_{l\_0}+1)} -
smatrix
in \mathbb{L} \mathbb{S}\_{t\_0 < s\_{0\*}} \tag{116}$$

$$\mathcal{Y}\_1 \text{ is semicircular in } \mathbb{L}\mathbb{S}\_{t\_0 \times s\_0 \prime} \tag{117}$$

*where* LS*t*0<*s*0*is the semicircular* [*t*0, *s*0]*-filtration.*

**Proof.** Let *X*1 and *Y*1 be given as above in LS, and fix *pl*0 ∈ {*p*1, ..., *pN*}. Note that, by the assumption, these operators *X*1 and *Y*1 form free sums in the semicircular filtration LS0, having *N*-many summands. Note also that they are self-adjoint in LS by the self-adjointness of their summands.

By (113), if an operator *T* has its non-zero free distribution in the semicircular [*t*0, *s*0]-filtration LS*t*0<*s*0 , where [*t*0, *s*0] is a *pl*0-neighborhood in R, then it must have its non-zero summand *T*0,

$$T\_0 \in \mathbb{L} \mathbb{S}\_{p\_{l\_0}} \text{ in } \mathbb{L} \mathbb{S}\_{t\_0 < s\_0}$$

.

By the very construction of *X*1 and *Y*1, they contain their summands,

$$
\mathbb{Q}\_{p\_{l\_0}, j\_{l\_0}, \prime} \oplus\_{p\_{l\_0}, j\_{l\_0}} \in \mathbb{L} \mathbb{S}\_{p\_{l\_0}} \text{ in } \mathbb{L} \mathbb{S}\_{t\_0 \times s\_0}.
$$

Consider now that:

$$\begin{array}{lcl} X\_1^{\mathfrak{n}} &=& \sum\_{(\mathring{\imath}\_1,\ldots,\mathring{\imath}\_n)\in\{1,\ldots,N\}^{\mathfrak{n}}} \left( \prod\_{k=1}^N Q\_{p\_{\mathring{\imath}\_k,\mathring{\jmath}\_k}} \right) \\ &=& Q\_{p\_{\mathring{l}\_0,\mathring{l}\_0}}^{\mathfrak{n}} + \sum\_{(\mathring{\imath}\_1,\ldots,\mathring{\imath}\_n)\neq(\mathring{l}\_0,\ldots,\mathring{l}\_0)} \left( \prod\_{k=1}^N Q\_{p\_{\mathring{k}\_l},\mathring{\jmath}\_k} \right) \\ &=& Q\_{p\_{\mathring{l}\_0,\mathring{l}\_0}}^{\mathfrak{n}} + [\text{Rest Terms}]\_{\prime} \end{array}$$

and similarly,

$$Y\_1^n = \Theta\_{p\_{l\_0}, j\_{l\_0}}^n + [\text{RestTerms}]',\tag{118}$$

.

for all *n* ∈ N.

> It is not difficult to check that:

$$
\pi\_{t\_0 < s\_0} \left( [\text{Rest Terms}] \right) = 0 = \pi\_{t\_0 < s\_0} \left( [\text{RestTerms}]' \right) \,\text{},\tag{119}
$$

by (98) and (113), where [Rest Terms], and [Rest Terms] are from (118).

Therefore, one obtains that:

$$\begin{aligned} \tau\_{t\_0 < \varsigma\_0} \left( X^n\_1 \right) &= \tau\_{t\_0 < \varsigma\_0} \left( Q^n\_{p\_{l\_0, \dot{l}\_0}} \right) = \tau^0\_{p\_{l\_0}} \left( Q^n\_{p\_{l\_0, \dot{l}\_0}} \right) \\ &= \tau^0\_{p\_{l\_0, \dot{l}\_0}} \left( Q^n\_{p\_{l\_0, \dot{l}\_0}} \right) = \omega\_n p\_{l\_0}^{2(\dot{j}\_{l\_0} + 1)} c\_{\frac{n}{2}} \end{aligned}$$

and, similarly,

$$
\pi\_{l\_0 < \varepsilon\_0} \left( Y\_1^n \right) = \pi\_{p\_{l\_0, \hat{l}\_0}}^0 \left( \Theta\_{p\_{l\_0, \hat{l}\_0}}^n \right) = \omega\_n \varepsilon\_{\frac{n}{2}}.\tag{120}
$$

for all *n* ∈ N, by (119).

Therefore, the free sum *X*1 ∈ LS is *p*2(*jl*0+1) *l*0 -semicircular in LS*t*0<*s*0 ; and the free sum *Y*1 ∈ LS is semicircular in LS*t*0<*s*0 , by (120). Therefore, the statements (116) and (117) hold true.

The above theorem shows that, if there is a free sum *T* in the semicircular filtration LS0 and if we "nicely" truncate the linear functional *τ*0 on LS, then one can focus on the non-zero summand *T*0 of *T*, whose the free distribution not only determines the truncated free distribution of *T*, but also follows the (weighted-)semicircular law.

### **11. Applications of Prime-Neighborhoods**

In Section 9, we considered the semicircular truncated-filtrations LS*t*<*s* for *t* < *s* ∈ R and studied how [*t*,*s*]-truncations on P affect, or distort, the original free-distributional data on the semicircular filtration LS0 = -LS, *τ*0. As a special case, in Section 10, we introduced *p*-neighborhoods for primes *p* and considered corresponding truncated free distributions on LS.

In this section, by using prime-neighborhoods, we provide a completely "new" model of truncated free probability on LS and study how the original free-distributional data on LS0 are distorted under this new truncation model.

Let us now regard the set P of all primes as a *totally ordered set* (a TOset),

$$\mathcal{P} = \{q\_1 < q\_2 < q\_3 < q\_4 < q\_5 < \dots\} \tag{121}$$

under the usual inequality (≤) on P, i.e.,

$$q\_1 = 2, q\_2 = 3, q\_3 = 5, q\_4 = 7, q\_5 = 11, \text{etc.}$$

For each *qk* ∈ P of (121), determine a *qk*-neighborhood *Bk*

$$B\_k \stackrel{donde}{=} [t\_k, s\_k] \\in \mathbb{R}\_\prime \tag{122}$$

for all *k* ∈ N.

Let *τBk*be our truncated linear functionals *τtk*<*sk*of (92) on the Banach ∗-algebra LS, i.e.,

$$
\pi\_{\mathbb{R}\_k} = \pi\_{l\_k \le s\_{k'}} \text{ for all } k \in \mathbb{N}. \tag{123}
$$

Then, by the truncated linear functionals of (123), one can have the corresponding semicircular *Bk*-filtrations,

$$\mathbb{LES}\_{\mathbb{B}\_k} = \mathbb{LES}\_{\mathbb{H}\_k \le s\_k} = \left(\mathbb{LES}, \,\,\tau \mathfrak{g}\_k\right), \tag{124}$$

for all *k* ∈ N.

> We now focus on the system:

$$\mathbf{T} = \{\tau \mathbf{z}\_k\}\_{k=1}^{\infty} \tag{125}$$

of *qk*-neighborhood-truncated linear functionals (123) for all *k* ∈ N.

Let *F* be a "finite" subset of the TOset P of (121), and for such a set *F*, define a new linear functional *τF* on LS induced by the system **T** of (125), by:

$$\tau\_{\mathcal{F}} = \sum\_{\emptyset \neq \mathcal{F}} \tau\_{B\_k} on \mathbb{L} \mathbb{S}. \tag{126}$$

Before proceeding, let us consider the following result obtained from (113).

**Lemma 5.** *Let p* ∈ P *and* [*t*, *s*] *be a p-neighborhood in* R, *and let* LS*t*<*s be the semicircular* [*t*, *s*]*-filtration. Let τ*0*p* = *j*∈Z*τ*0*p*,*j be the linear functional* (81) *on the Banach* ∗*-subalgebra* LS*p of* (82) *in the semicircular filtration* LS0. *Define a linear functional τp on the Banach* ∗*-algebra* LS *by:*

$$
\pi^p(T) \stackrel{def}{=} \begin{cases}
\pi\_p^0(T) & \text{if } T \in \mathbb{L}\mathbb{S}\_p \text{ in } \mathbb{L}\mathbb{S}, \\
O(T) = 0 & \text{otherwise},
\end{cases}
$$

*for all T* ∈ LS. *Then, the Banach* ∗*-probability space* (LS, *τp*) *is free-isomorphic to* LS*t*<*s*, *i.e.,*

$$[t, s] \text{ is a } p-m \text{-} neighborhood \implies \mathbb{L} \mathbb{S}\_{t \le s} \text{ and } (\mathbb{L} \mathbb{S}, \ \mathbf{r}^p) \text{ are free}-isomorphic. \tag{127}$$

**Proof.** Under the hypothesis, it is not hard to check:

$$
\pi\_{t < s} = \tau^p \text{ on } \mathbb{L}\mathbb{S}.
$$

Therefore, the identity map on LS becomes a free-isomorphism from LS*t*<*s* onto (LS, *τp*).

If a finite subset *F* is a singleton subset of P, then the free probability on LS determined by the corresponding linear functional *τF* of (126) is already considered in Section 10 and in (127). Therefore, we now restrict our interests to the cases where finite subsets *F* have more than one element in P.

**Lemma 6.** *Let F be a finite subset of the TOset* P *of* (121)*, and let τF be the corresponding linear functional* (126) *on* LS. *Then:*

$$\pi\_{\mathcal{F}} = \sum\_{\emptyset \neq \mathcal{F}} \pi^{\emptyset \mathbb{k}} on \mathbb{L} \mathbb{S}, \tag{128}$$

*where τqk are in the sense of* (127)*.*

**Proof.** The proof of (128) is done by (126) and (127) because:

$$(\mathbb{L}\mathbb{S}, \tau^{q\_k}) \text{ and } \mathbb{L}\mathbb{S}\_{B\_{k}}$$

are free-isomorphic for all *qk* ∈ *F*. Therefore, the linear functional *τF* of (126) satisfies that:

$$\mathsf{TF} = \sum\_{q\_k \in F} \mathsf{\tau}\_{\mathsf{B}\_k} = \sum\_{q\_k \in F} \mathsf{\tau}^{q\_k} \text{ on } \mathsf{L}\mathbb{S}.$$

By (113), (116), (117), and (128), one obtains the following result.

**Theorem 12.** *Let T* = *N* Π *l*=1*Qnl pl*,*jl or S* = *N*Π*l*=1Θ*nl pl*,*jl be a free reduced word of* LS *with its length-N*, *for N* ∈ N*. If: F* ∩ {*p*1, *..., pN*} = ∅ *in* P,

*then:*

$$
\tau\_{\mathbb{F}}(T) = 0 = \tau\_{\mathbb{F}}(S). \tag{129}
$$

*While, if F* ∩ {*p*1, ..., *pN*} = ∅ *in* P, *then:*

> *τF*(*T*) = ∑ *q*∈*F*∩{*p*1,...,*pN*} *ωnq*2(*j*+1)*c n*2 ,

*respectively,*

$$\pi\_{\mathcal{F}}(S) = |F \cap \{p\_{1\prime}, \dots, p\_N\}| \left(\omega\_n \mathfrak{c}\_{\frac{n}{2}}^n\right) \,. \tag{130}$$

*where* |*X*| *mean the cardinalities of sets X*.

**Proof.** Let *T* and *S* be given free reduced words with their length-*N* in LS, for *N* ∈ N. If:

$$F \cap \{p\_{1\prime}, \dots, p\_N\} = \mathcal{Q} \text{ in } \mathcal{P}\_{\prime}$$

then we obtain the formula (129) by (127) and (128). Indeed,

$$\tau\_F(T) = \sum\_{q \in F} \tau^q(T) = 0 = \sum\_{q \in F} \tau^q(S) = \tau\_F(S).$$

Now, assume that:

$$F \cap \{p\_{1\prime}, \dots, p\_N\} = \{p\_{i\_1 \prime}, \dots, p\_{i\_k}\} \text{ in } \mathcal{P}\_{\prime \prime}$$

for some *k* ∈ N, such that 1 ≤ *k* ≤ *N*. Then:

$$\pi\_F(T) = \left(\sum\_{l=1}^k \pi\_{p\_{i\_l}}^0\right)(T) = \sum\_{l=1}^k \pi\_{p\_{i\_l}}^0(T).$$

by (126) and (128)

$$\begin{split} \boldsymbol{\tau} &= \boldsymbol{\Sigma}\_{l=1}^{k} \boldsymbol{\tau}\_{p\_{\dot{\boldsymbol{\eta}}}}^{0} \left( \boldsymbol{Q}\_{p\_{\dot{\boldsymbol{\eta}}\_{l}}, \dot{\boldsymbol{\eta}}\_{l}}^{n\_{\boldsymbol{\eta}\_{l}}} \right) = \boldsymbol{\Sigma}\_{l=1}^{k} \, \boldsymbol{\tau}\_{p\_{\dot{\boldsymbol{\eta}}\_{l}}, \dot{\boldsymbol{\eta}}\_{l}}^{0} \left( \boldsymbol{Q}\_{p\_{\dot{\boldsymbol{\eta}}\_{l}}, \dot{\boldsymbol{\eta}}\_{l}}^{n\_{\boldsymbol{\eta}\_{l}}} \right) \\ &= \boldsymbol{\Sigma}\_{l=1}^{k} \left( \boldsymbol{\omega}\_{\boldsymbol{\eta}\_{l}} p\_{\boldsymbol{\eta}\_{l}}^{2(j\_{l}+1)} c\_{\frac{\boldsymbol{\eta}\_{l}}{2}} \right) . \end{split} \tag{131}$$

Similarly,

$$\pi\_{\mathcal{F}}(S) = \sum\_{l=1}^{k} \left( \omega\_{n\_l} c\_{\frac{n\_l}{2}} \right) = k \cdot \left( \omega\_{n\_l} c\_{\frac{n\_l}{2}} \right).$$

Therefore, the free-distributional data (130) hold.

The above free-distributional data (129) and (130) characterize the free-probabilistic information on Banach ∗-probability spaces

> (LS, *τF*),

for any finite subsets *F* of P.

**Author Contributions:** The authors contributted equally in this article.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.


**5. Conclusions**

For many experts, the best indicators of the effectiveness of health services are *indicators of Health-Related Quality of Life (HRQoL), wellbeing and citizen satisfaction*. These indicators all measure global outcomes in patients and in the population, since *quality of life and well-being* have multidimensional values and account for the perspective of the patient undergoing the clinical and/or surgical interventions, procedures and services which are recommended and prescribed by practitioners, with informed consent, such as treatment and/or functional recovery and rehabilitation.

The **generic surveys** recommended for the assessment of HRQoL as an indicator are those which grant a comprehensive perspective on patients based on the Biopsychosocial Model of Health, placing patients in the main role of the outcome.

Of these surveys, the most widely used at the international level is SF-36 due to quality criteria and because, **it is used as a reference instrument and because** and it allows more comparisons, giving greater consistency to outcomes obtained at different healthcare and social/health centres and across different countries. Alternative questionnaires exist which may be used based on patients and their health and social circumstances.

Alternative questionnaires are available such as the Nottingham Health Profile (NHP) that is better when measuring health impact in populations, or the SIP when one wants to know the perception of illness that patients refer, the main drawback being it has 136 items, thus not recommended in elderly patients. Specific questionnaires can be used based on patient characteristics. If these are chronic, the Quality of Life Profile for Chronically Ill patients (PLC) is a good option. Based on the objectives, if functional capacity is to be assessed, The *Duke* Activity Status *Index (DASI)* is valid, reliable, and sensitive. It is also predictive in patients with cardiovascular alterations, which was its first use. If you want to estimate psychological or mental well-being, the Psychological General Well-Being Index (PGWBI) is appropriate.

On the other hand, all of these questionnaires can be self-administered. Still, patient's cognitive characteristics must be taken into account, basically that they can read and understand the questions correctly so that answers are reliable.

The **goal** of using these questionnaires when assessing HRQoL is the conversion of evidence into effective results which increase patient quality of life and wellbeing, as health is a fundamental resource for life, and this requires applied or clinical research and a public health system for the improvement of quality of care, HRQoL, and wellbeing.

*Modifiers of Health-Related Quality of Life by Biological, Psychological and Social… DOI: http://dx.doi.org/10.5772/intechopen.97451*


**5. Conclusions**

The applied analysis methods enabled the characterization of the present material structures of the investigated slag samples. Through the synergetic e ffect of the two imaging techniques (SEM-based image analysis and X-ray CT), it was possible to identify potential valuable phases and assess the recyclability of these contents. The application of these imaging techniques improves the understanding of the size, shape, and association of the present phases. The Cu-metal contents within the slag samples represent the main valuable component. For a sustainable recycling of these contents, the slag structure has to be optimized and adjusted to the requirements of following processes with the help of various process parameters (e.g., cooling rate). The detailed characterization of the slag structure by imaging processes in combination with fluid flow modeling approaches via computational fluid dynamics represents the basis for an adjusted process optimization and further improvement of recyclability. The main conclusions from the present study in short are as follows:

**Author Contributions:** M.B. conceptualized the paper. N.B. was responsible for the metallurgical tests. T.H. was responsible for sample analysis with a mineral liberation analyzer (MLA) including quality control, data processing, and data evaluation. T.L. was responsible for sample analysis with X-ray computed tomography (XCT) including quality control, data processing, and data evaluation. M.B. and T.L. were responsible for the grinding tests of the material. M.B., N.B., T.L., and T.H. analyzed, interpreted, and collated all results. M.A.R., B.F., and U.A.P. interpreted the results, supervised the work, and supported the preparation of the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors would like to thank the German Research Foundation (DFG) for funding of the X-ray microscope (Zeiss Xradia 510 Versa) INST 267/129-1.

**Conflicts of Interest:** The authors declare no conflicts of interest.


3.3.1. Drying Methods

Freeze-drying (FD, control) (ca. 100 g) was carried out in a freeze dryer (Christ Alpha 1–4 LSC; Osterode am Harz, Germany) for 24 h. The temperature within the drying chamber was −60 ◦C, while the heating plates had the temperature of 25 ◦C.

Vacuum drying (VD) was made in VACUCELL 111 ECO LINE vacuum dryer (MMM Medcenter Einrichtungen GmbH, Planegg, Germany) at 50 and 60 ◦C under pressure of 0.1 mbar for 24, and 16 h, respectively.

All drying experiment were performed in duplicate. The samples obtained were milled by laboratory mill (IKA A.11, Wilmington, NC, US), and vacuum sealed. The powders were kept in a freezer (−20 ◦C) until extracts' preparation.


**Abstract**

Differentiated thyroid carcinoma (DTC) represents more than 90% of all thyroid cancer histological types. Its incidence has increased at a faster rate than most other malignancies during the last three decades and varies considerably around the world. The familial form of the disease has also become more common than previously reported, accounting for 5−15% of DTC cases. The main established risk factor of thyroid cancer is exposure to ionizing radiation, particularly if occurred during childhood. Thyroid cancer (including DTC) is also characterized by having one of the highest familial risks of any cancer supporting heritable predisposition. In spite of such a high familial risk, linkage analysis in non-syndromic DTC families (i.e. families where DTC is the primary cancer) performed two decades ago mapped several susceptibility loci but did not lead to the identification of high-penetrance causal germline variants. More recently, genome-wide association studies based on population case–control studies identified a limited number of DTC-associated loci and suggested that multiple low penetrance genes are involved in predisposition to DTC. This chapter reviews known genetic factors predisposing to DTC as well as approaches used to map them in various populations, and opens up on alternative strategies that could help to understand DTC tumorigenesis.

**Keywords:** differentiated thyroid cancer, familial risk, case–control study, genetic predisposition, genome-wide association study


**14. SCI patient rehabilitation stages through time**

#### **14.1 Acute phase**

This rehabilitation begins since the patient is admitted to the hospital until the stabilization. It can be a period of 6–12 weeks, depending on the existence of complications. Rehabilitation in the acute phase is important to increase the patient strength and stability for postural adaptation and orthostatic hypotension [19, 28].

Passive exercises have been observed to decrease the risk of spasticity [43]. Other early interventions in rehabilitation are bed mobility with rotation at 2–3-h intervals to prevent pressure ulcers [19, 34].


**Observation of Dispersion in the Japanese Coastal Area of Released 90Sr, 134Cs, and 137Cs from the Fukushima Daiichi Nuclear Power Plant to the Sea in 2013**

**Hirofumi Tazoe 1,\*, Takeyasu Yamagata 2, Kazuki Tsujita 3, Hisao Nagai 2, Hajime Obata 4, Daisuke Tsumune 5, Jota Kanda 6 and Masatoshi Yamada 1,7**

Received: 30 September 2019; Accepted: 22 October 2019; Published: 24 October 2019

**Abstract:** The March 2011 earthquake and tsunami resulted in significant damage to the Fukushima Daiichi Nuclear Power Plant (FDNPP) and the subsequent release of radionuclides into the ocean. Here, we investigated the spatial distribution of strontium-90 (90Sr) and cesium-134/cesium-137 ( 134, 137Cs) in surface seawater of the coastal region near the FDNPP. In the coastal region, 90Sr activity was high, from 0.89 to 29.13 mBq L−1, with detectable FDNPP site-derived 134Cs. This indicated that release of 90Sr from the power plant was ongoing even in May 2013, as was that of 134Cs and 137Cs. 90Sr activities measured at open ocean sites corresponded to background derived from atmospheric nuclear weapons testing fallout. The FDNPP site-derived 90Sr/ 137Cs activity ratios in seawater were much higher than those in the direct discharge event in March 2011, in river input, and in seabed sediment; those ratios showed large variability, ranging from 0.16 to 0.64 despite a short sampling period. This FDNPP site-derived 90Sr/ 137Cs activity ratio suggests that these radionuclides were mainly derived from stagnant water in the reactor and turbine buildings of the FDNPP, while a different source with a low 90Sr/ 137Cs ratio could contribute to and produce the temporal variability of the 90Sr/ 137Cs ratio in coastal water. We estimated the release rate of 90Sr from the power plant as 9.6 ± 6.1 GBq day−1 in May 2013 on the basis of the relationship between 90Sr and 137Cs activity ( 90Sr/ 137Cs = 0.66 ± 0.05) and 137Cs release rate.

**Keywords:** Fukushima Daiichi Nuclear Power Plant; strontium-90; cesium-137; seawater monitoring; contaminated water


**2. Microwave thermotherapy**

The first four of the following list of thermotherapeutical applications are just largely used in many countries around the world; the last three instead are at this moment in the phase of very promising projects:

• Oncology (cancer treatment)

Biological principle utilizes the fact that certain tumor cells are very sensitive to a temperature higher than 41°C, while normal cells generally survive elevated

temperatures up to 45°C. And so heating of the tumor region at temperatures of 41– 45°C can selectively destroy tumor cells.

• Physiotherapy (treatment of rheumatic and skeletal diseases)

Like in hyperthermia, therapeutic effect is caused by the principle of heating biological tissue, but to lower temperatures—usually only up to 41°C. It is used for treating pain in certain rheumatic and degenerative diseases and the treatment of chronic inflammations resistant to antibiotics, often used in rehabilitation and physical therapy.

• Urology (BPH treatment)

Microwave thermocoagulation—heating up to temperatures much higher than 45°C, usually around 70°C. An example can be given the microwave treatment of Benign Prostate Hyperplasia, which can replace a complicated surgery.

• Cardiology (arrhythmia and fibrillation treatment, microwave angioplasties)

Cardiac catheter thermal ablation is now the standard of care for various cardiac arrhythmia types (irregular heartbeat rhythm). The method uses a catheter terminated with a microwave antenna, which is introduced into either heart of the patient or into partially or totally blocked blood vessels. Heat gained by microwave energy either safely removes the cells inside the human heart causing arrhythmia and/ or fibrillation or removes sclerotic plaques deposited on the walls of blood vessels.

For here mentioned thermotherapy treatments, it is important to mention that frequencies from the frequency band started approximately at 1 MHz and going up to 10 GHz are mostly used. This frequency range is given by the optimal depth of penetration of EM waves into biological tissue. Thus, this frequency band can achieve the needed depth of effective treatment.


**4.5. Population expansion of Tibetan sheep populations**

The mismatch distribution analysis of the complete dataset, maternal lineages A, B, C, D, and 15 Tibetan sheep populations of the mtDNA D-loop, is presented [29]. Neutrality tests (Ewens-Watterson test, Chakraborty's test, Tajima's D test, Fu's FS test) were used to detect population expansion [29]. The complete dataset of all Tibetan sheep populations had a significantly large negative Tajima's D value and *FS* value. This result shows two large and sudden expansions, consistent with a demographic model, as inferred from the mismatch distribution. The mismatch distribution of the complete dataset suggested that there were two major peaks with maximum values at 4 and 27 pairwise differences and two smaller peaks at 45 and 51 differences. Based on the results, it could be implied that there are at least two expansion events occurred in the population demographic history of the Tibetan sheep, which live on the Qinghai-Tibetan Plateau. The mismatch distribution analysis revealed a unimodal bell-shaped distribution of the pairwise sequence differences in maternal lineages A, B and C. However, the distribution of maternal lineage D was a sambong function, duo to the geographic distribution patterns of species diversity. Mismatch analysis of maternal lineages A, B, and C suggested that it happened in the demographic history of Tibetan sheep populations that single population expansion events occurred before. Similar results were found in previous reports [42, 43].

showed that four maternal lineages (A, B, C and D), previously defined, could be identified in the 636 tested individuals of the 15 Tibetan sheep populations. The estimation of demographic parameters from the mismatch analyses shows that maternal lineages A, B and C had at least one demographic expansion in the Tibetan sheep of the Qinghai-Tibetan Plateau

Phylogenetic Evolution and Phylogeography of Tibetan Sheep Based on mtDNA D-Loop Sequences

http://dx.doi.org/10.5772/intechopen.76583

147

The authors appreciated constructive comments from the editor Hervé Seligmann. This work was supported by the special fund from the Major International (Regional) Joint Research Project (NSFC-CGIAR<PHONE_NUMBER>0), and Gansu Provincial Agricultural biotechnology research and application projects (GNSW-2014-21, GNSW-2016-13), and the Central Level,

This study did not involve endangered or protected Tibetan sheep populations. All experimental and sampling procedures were approved by the Institutional Animal Care and Use Committee, Lanzhou Institute of Husbandry and Pharmaceutical Sciences, Peoples Republic

Conceived and designed the experiments: LJB DXZ ZYF GX SXP. Performed the experiments: LJB DXZ ZYF GX SXP. Analyzed the data: GX SXP YC. Wrote the paper: LJB DXZ ZYF GX YC.

1 Lanzhou Institute of Husbandry and Pharmaceutical Sciences of the Chinese Academy of

2 Sheep Breeding Engineering Technology Research Center of Chinese Academy of

, Xian Guo1†‡

, Xiaoping Sun1,2†‡

and

, Yufeng Zeng1†‡

Scientific Research Institutes for Basic R & D Special Fund Business<PHONE_NUMBER>016).

areas.

**Acknowledgements**

**Conflict of interest**

**Author contributions**

\*, Xuezhi Ding1†‡

Agricultural Sciences, Lanzhou, China

Agricultural Sciences, Lanzhou, China

\*Address all correspondence to<EMAIL_ADDRESS>
These authors contributed equally to this work

These authors are co-first authors on this work

**Author details**

Jianbin Liu1,2†‡

Chao Yuan1,2†‡

†

‡

of China.


**4. The purpose of using social media in higher education**

For educational environments to be improved by encouraging creative thinking and innovative action, state education strategies often foresee measures for the development and expansion of e-learning, the introduction of expert teaching systems and other modern teaching methods based on information and communication technology, the dynamic development and application of which radically change the paradigms of learning and education, with impacts and consequences that are difficult to predict on future ways of acquiring, transferring and applying knowledge, skills, values, and attitudes [7].

On the trail of such measures, the range of social media enables a wide range of possible purposeful ways of use, and in addition, they are constantly increasing and generating new possibilities of use. Some possible purposes are listed in the following **Table 2**.

#### **Table 2.**

*Purposes of using social media in higher education [3].*

The globe has become smaller because of social media, according to Raut and Patil in 2016 [8]; people have access to more knowledge, information, and opportunities to apply it. With their aid, it is now feasible to process material that would have been too difficult for humans to understand just 20 years ago, and in addition to speeding up our education and training, talents are also identified more quickly [8]. They have also increased our ability to absorb information.

Social media use in higher education is subject to both pro and con arguments.

### **5. General implications of the use of social media in higher education**

The main educational implication of social media is the seemingly changing nature of the relationship between students and information and knowledge. The epistemological tenets of formal education and tailored instruction are fundamentally different from the modes of knowledge generation and consumption that social media promote [9]. These changes are embodied in Thomas and Seely Brown's [10] description of a technology-enhanced "new culture of learning"—that is, learning based on the principles of collective inquiry, play, and innovation rather than individualized instruction. The generation of today's students has organically grown up with social media. Additionally, they have little knowledge of a world without computers, smartphones, or social media. A technology that has been widely embraced by students is social media, which has the potential to be a useful tool for boosting communication in the classroom and student cooperation with professors [11].

However, several studies show that there is a digital divide between students and their educational institutions; students are willing to use them, and faculty employees are not [12].

To investigate in practice whether this is the case, that is, what affects teachers" use of social media, a survey was conducted in 2019.


**5. Real-world use case: methodology and results**

Vezeshari is a poultry and eggs farm from Zhelino, North Macedonia. They have chosen Xively (software by LogMeIn) for their needs and working processes, as well as their Xively IoT platform. By these, they can monitor the internal air temperature, air humidity, CO2 amount, and water nutrient level, and also –get a history of security alerts (**Figure 5**). Security, scalability, and expertise are important deciding factors, and by choosing an IoT solution, Vezeshari can now handle the entire network of connections. They also have overview and support for different scenarios, while getting the best guidance and advice from professionals (Xively).

By getting secure, reliable, and fast access, Vezeshari maintenance team can now excel in other areas of the farm and overall business:

*Methods for Detection and Prevention of Vulnerabilities in the IoT (Internet of Things) Systems DOI: http://dx.doi.org/10.5772/intechopen.113898*

#### **Figure 5.**

*Chicken farm application—allows monitoring of internal air temperature, air humidity, CO2 amount, water nutrient level, as well as a history of alerts (presented graphically).*

• Vezeshari employees have insight into day-to-day farm activities that gives them the ability to proactively meet customer needs, while also growing their business by selling consumables that are needed quickly based on farm usage.

Today, the entire Vezeshari working process is supported by state-of-the-art systems for detection and prevention of attacks that are updated and optimized daily. Thus, they achieve protection that is reliable even against the biggest threats and attacks in the system. Attack detection and prevention systems are composed of various antivirus and antispyware software, as well as the latest versions of firewalls for protection. Other methods using an increased level of security and data encryption, such as protection of the smartphone and tablet applications themselves through various types of generated passwords, are used in order to enable the detection and prevention systems to successfully recognize and prevent attacks in the systems.

To test the resilience of Vezeshari's network, we have implemented signaturebased IDS (intrusion detection system). We used Snort—open-source signaturebased IDS—and we have set up its rules to detect the following types of attacks:

To test our IDS, we invited ethical hackers from several countries (Hungary, Israel, France, USA, Netherlands) *via* forums and mailing lists (total of 56 participants). The attackers utilized code injections that targeted the wireless layer of the IoT system. The wireless frames from different Wi-Fi components of the IoT system are prone to these attacks—so we tested injection attacks at these points. To test our IDS, the ethical hackers conducted orchestrated attack attempts from multiple locations.

We've installed and configured Snort software in accordance with [17]. We opened the extracted folder *snortrules* then navigated to the *etc* folder and copied the snort. conf file then pasted it in *C:Snortetc* folder. Next we moved the folders so\_rules, preproc\_rules to the *C:Snort* directory path.

We entered and enabled the rules set before launching Snort, that is, we enabled ICMP rules so that Snort can detect any ping probes to the system while running. For example, a rule to detect a suspicious TCP intrusion (access rule) is in the form:

alert tcp any any -> any any (msg:"Suspicious User-Agent detected"; flow:to\_ server,established; content:"User-Agent|3a| "; nocase; content:"curl|2f|";nocase; sid:1000002; rev:1;)

The Snort software was operating in real time and results of the intrusion detection testing are presented in the following table (**Table 2**).

As we can see from the table, our IDS was able to successfully detect and alert on the attack attempts in most of the cases (over 80%). The most successful our system was for the firmware command injection attacks (95.3%), and the least successful in case of XML injection attacks. The rate of success varies for different attacks, because of the different capability to hide the harmful code within the legitimate IP packets. (The Snort rules can easily detect a harmful code within the firmware commands, rather than within XML code.)

The results indicate that our IDS for detection and prevention of attacks should be updated and optimized weekly, in order to achieve reliable and robust protection even against the most current threats and attacks, especially for this new IoT technology.

Of course our approach (usage of signature-based detection and Snort) has potential limitations, such as the following:

#### **Table 2.**

*Detection rate of four different types of attacks.*

*Methods for Detection and Prevention of Vulnerabilities in the IoT (Internet of Things) Systems DOI: http://dx.doi.org/10.5772/intechopen.113898*

To overcome these limitations we plan to extend our IDS by implementing an anomaly-based detection as the one elaborated in [10] by Tacker et al., and we are discussing this possibility in the last section of this paper (future work).

## **6. Conclusion and future work**

The Internet of Things, which is also called the fourth industrial revolution, truly deserves that name. The tendency of IoT is to connect all disconnected devices. Today, life without the Internet of Things is unimaginable. Numerous devices from households, (air conditioners, lighting, video surveillance) to numerous devices in practically all industries (agriculture, healthcare, finance, energy, the automotive industry etc.), in order to improve the quality of life and increase economic growth, are interconnected, integrated and share data in real-time with the help of networks of all networks, the Internet.

But there is also a real danger that these devices will be exposed to cyber-attacks and that the confidentiality, integrity, and availability of data will come into question. IoT devices generate a large amount of data; therefore the question of the security of these devices and the entire IoT ecosystem arises, as well as the question of privacy.

Of course, as for everything else, it is necessary to carry out a risk assessment, from the identification of the resource, the vulnerability of the resource itself, possible threats that can exploit the vulnerability, and in the case of an attack, to determine the consequences that the attack could cause. The practice has shown the vulnerability of IoT devices due to several reasons, from the very physical characteristics of the devices, which are small in size, mostly untested for safety before use, low price, and low energy consumption. It is this sensor layer that is most at risk, in contrast to the access, network and application layers, where the risk is mostly assessed as low to medium.

Also, IoT technologies are not followed by legislation either, only in the last two to three years have societies recognized the problem and become aware of the risks and started the process of establishing a legislative and standardization framework that will regulate the IoT area.

The only way to stop attacks is to know the techniques used to attack. Therefore, organizations' security systems will need to adopt the most robust model or mechanism that provides the strongest protection against threats to ensure that the system remains secure. The attack detection and prevention system (IDS/IPS) ensures that attacks are detected and prevented using multiple approaches. Active attack detection and prevention systems aim to limit the damage that attackers can cause by building a local network that is resistant to the appropriate attack or threat.

In the last section of the paper, we presented a real-world use case (a poultry farm) that has acquired an IoT solution (Xively) and is now able to monitor the internal air temperature, air humidity, CO2 amount, water nutrient level, and get a history of security alerts that now can be controlled. At Vezeshari, we have implemented an open-source IDS in Snort to detect four types of IoT attacks: dynamic login attempts, XML injection attacks, SQL injection attacks, and Firmware (command) injection

attacks. All of these attacks utilize code injections that target the wireless layer of the IoT system. The wireless frames from different Wi-Fi components of the IoT system are prone to these attacks so we tested injection attacks at these points.

To test our IDS we invited ethical hackers from multiple countries that conducted orchestrated attack attempts. In most of the cases (over 80%) our IDS was able to detect and alert on the attack attempts, and the results are presented in Section 5. The rate of success varies for different attacks, because of the different capabilities to hide the harmful code within the legitimate IP packets. Therefore, our system for detection and prevention of attacks should be updated and optimized weekly, to achieve reliable and robust protection even against the biggest threats and attacks in the system, especially in a new branch of technology such as the Internet of Things.

In future work, we plan to extend our IDS by implementing anomaly-based detection, i.e. by utilizing machine learning techniques. Anomaly-based IDS-s require larger processing resources, but they are superior in the detection of new, previously unknown threats. They are also adaptive and dynamic, as they can learn from the network behavior and update the baseline accordingly. There are eight methods for detecting traffic anomalies in real-time data, namely: projection-based methods, regression-based methods, support vector machines, decision tree–based methods, density-based methods, clustering, distance-based, and time series–based methods.

We plan to apply support vector machines [18] and decision trees [19]. Both of these machine learning methods are based on training the detector (IDS system), which will learn and be able to detect the real anomalies (intrusions). In the testing phase, a new data set will be used to develop the system's capacity to generalize to previously unseen intrusions. Support Vector Machine (SVM) method is a classification approach where support vectors form the boundaries of a class. In detecting anomalies, a single-class SVM will be used to define a normal class, and points that are outside the class boundaries can be defined as anomalies. Tree-based methods create a tree structure from data, where the tree will be updated with new data, but if new data causes significant changes in the tree structure, the model needs to be re-trained.

The field of IoT security is a contemporary and dynamic field of research. The broader significance of our research is that we implemented a cost-effective IDS in a real poultry farm. Our findings presented in this paper illustrate an IDS that is affordable and easy to implement in many small and medium businesses. We proved that the IoT system should not be put in function without providing its security. Our system is able to detect multiple threats, including DoS (denial of service) and malware (virus attacks). Our ultimate goal will be to develop an autonomous IDS and apply state-of-the-art techniques of machine learning and deep learning that can learn from the big IoT data. In addition, such future IoT IDS would have features such as self-configuration, self-optimization, self-protection, and self-healing.

*Methods for Detection and Prevention of Vulnerabilities in the IoT (Internet of Things) Systems DOI: http://dx.doi.org/10.5772/intechopen.113898*


**2. Background**

EI has witnessed a significant surge in growth lately, being intrinsically tied to the progression of edge computing. However, at the beginning of the ubiquitous and pervasive computing era, there was a significant deficiency of intelligence at the network's edge in favor of a "remote" intelligence. For example, the primary function of Wireless Sensor Networks (WSNs) [9] was to gather and transmit data according to the "sense-and-forward" paradigm, by means of dumb sensors that were relatively simplistic and resource limited. Therefore, cloud computing emerged as a prevalent enabler for supporting WSNs due to its ability to provide scalable data storage and management, remote monitoring and control, and ease of use. Both WSNs and cloud computing have started, hence, to take advantage of one another: the former found the necessary computing power for implementing intelligent solutions to be fed with a huge amount of real-time data provided by the latter.

As the IoT has gained traction [10], a plethora of more sophisticated devices, known as "smart objects", emerged at the periphery of the network. These devices, such as smart thermostats, security cameras, and connected appliances, promised to make our lives easier by automating daily tasks and providing valuable insights. However, despite their improved capabilities, these devices continued to be heavily reliant on cloud-based infrastructure [11]: indeed, devices still remained unable to take actions without the assistance of the cloud since both the volume and the heterogeneity of the data increased dramatically, and consequently, only simple processing tasks and limited storage operations could be performed locally.

Only in the last decade, a number of issues about the IoT–cloud duo has emerged and pushed for a paradigm shift: indeed, while cloud-based infrastructure does provide the necessary scalability and flexibility for IoT devices, it also introduces a number of

challenges. One major concern is the potential for data breaches and privacy violations, as sensitive information is transmitted to and stored on remote servers. Additionally, the reliance on cloud-based infrastructure can also result in unacceptably high latency in field-to-cloud and back transmissions, as well as exorbitant energy and bandwidth consumption. To address these issues, new computing paradigms such as edge and fog computing have emerged, with the intent to carry not only data processing, but more broadly, intelligence (intended as "Interacting, Interoperate, Cooperation, Communicating and Perception" capabilities [12]) as close as possible to the data sources, in the place of remote servers accessed over the Internet.

In this direction, more recently, EI has emerged in order to support the new and ambitious services and scenarios of the IoT. It incorporates both emerging and well-established approaches from edge and cloud computing, AI, data science, and networking to bring intelligence outside the boundaries of the cloud. This approach, also referred to as "Edge AI", pushes as much as possible for local operations, even better if directly on edge devices, such as smartphones, IoT devices, and industrial equipment, rather than in the cloud or a centralized data center. As illustrated in Figure 1, this strategy effectively reduces the amount of data transmitted from the device monitoring a target phenomenon to a remote server, thus reducing the time and the communication that pass between the operations of sensing and actuation. However, the challenge of EI involves not only embedding the characteristics of massive computing systems into tiny, restricted devices, as if trying "to fit an elephant into a small box" [13], but indeed, a full-fledged infrastructure to allow EI, at its extreme, to transform Big Data into intelligent data and to enable real-time device management, system performance, decision-making, and operation monitoring, thus improving overall responsiveness, privacy, effectiveness, and productivity [12,14–16]. Although EI holds the potential to rival the cloud, it cannot maximize its capabilities when employed alone. EI and cloud computing can complement each other seamlessly, with the optimum approach being a synergistic relationship, exemplified by the IoT–edge–cloud continuum [17]. This harmonious connection is crucial in today's technological arena, resulting in enhanced resource utilization, heightened efficiency, and the best outcomes.

**Figure 1.** From remote (e.g., cloud-based) to local (e.g., EI) data processing.


**Peng Li 1,2,3,\*, Xinhua Zhang 1,3,4 and Wenlong Zhang 4**

Received: 28 February 2019; Accepted: 26 April 2019; Published: 29 April 2019

**Abstract:** The traditional passive azimuth estimation algorithm using two hydrophones, such as cross-correlation time-delay estimation and cross-spectral phase estimation, requires a high signal-to-noise ratio (SNR) to ensure the clarity of the estimated target trajectory. This paper proposes an algorithm to apply the frequency diversity technique to passive azimuth estimation. The algorithm also uses two hydrophones but can obtain clear trajectories at a lower SNR. Firstly, the initial phase of the signal at different frequencies is removed by calculating the cross-spectral density matrix. Then, phase information between frequencies is used for beamforming. In this way, the frequency dimension information is used to improve the signal processing gain. This paper theoretically analyzes the resolution and processing gain of the algorithm. The simulation results show that the proposed algorithm can estimate the target azimuth robustly under the conditions of a single target (SNR = −16 dB) and multiple targets (SNR = −10 dB), while the cross-correlation algorithm cannot. Finally, the algorithm is tested by the swell96 data and the South Sea experimental data. When dealing with rich frequency signals, the performance of the algorithm using two hydrophones is even better than that of the conventional broadband beamforming of the 64-element array. This further validates the effectiveness and advantages of the algorithm.

**Keywords:** direction of arrival estimation; frequency diversity; passive sonar