Preventing Neurodegenerative Memory Loss in Hopfield Neuronal Networks Using Cerebral Organoids or External Microelectronics

<div>Execute memory recovery. (a) Damage in the original network severs connections and causes memory loss. Connectivity matrix <svg height="18.1689pt" id="M21" style="vertical-align:-6.1403pt" version="1.1" viewbox="-0.0498162 -12.0286 34.4831 18.1689" width="34.4831pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,12.131,-3.001)"><path d="M846 629L831 655C777 615 719 595 640 595C573 595 518 604 436 619C338 640 291 647 226 647C158 647 71 626 0 558L15 532C79 570 138 592 218 592C292 592 340 582 410 569C495 552 560 540 629 540C701 540 788 559 846 629Z" id="g119-114"></path></g><g transform="matrix(.013,0,0,-0.013,11.263,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z" id="g13-85"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.99,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.99,3.784)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path></g><g transform="matrix(.0091,0,0,-0.0091,26.492,3.784)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path></g><g transform="matrix(.0091,0,0,-0.0091,31.378,3.784)"><path d="M139 535C170 535 192 560 192 589C192 621 169 644 140 644C109 644 86 621 86 589C86 560 110 535 139 535ZM35 387C99 379 105 374 105 307V114C105 22 103 -35 96 -78C89 -113 82 -131 70 -146C55 -162 30 -174 -1 -181C-16 -184 -23 -192 -23 -207C-23 -232 0 -253 15 -253C24 -253 33 -249 41 -242C63 -223 127 -148 162 -48C181 6 186 47 186 117V453C143 435 93 422 36 414L35 387Z" id="g58-104"></path></g></svg>. (b) Connections from the original to the auxiliary network are activated. Connectivity matrix <svg height="18.1689pt" id="M22" style="vertical-align:-6.1403pt" version="1.1" viewbox="-0.0498162 -12.0286 34.4831 18.1689" width="34.4831pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,12.131,-3.001)"><path d="M846 629L831 655C777 615 719 595 640 595C573 595 518 604 436 619C338 640 291 647 226 647C158 647 71 626 0 558L15 532C79 570 138 592 218 592C292 592 340 582 410 569C495 552 560 540 629 540C701 540 788 559 846 629Z" id="g119-114"></path></g><g transform="matrix(.013,0,0,-0.013,11.263,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z" id="g13-85"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.99,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.99,3.784)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path></g><g transform="matrix(.0091,0,0,-0.0091,26.492,3.784)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path></g><g transform="matrix(.0091,0,0,-0.0091,31.378,3.784)"><path d="M139 535C170 535 192 560 192 589C192 621 169 644 140 644C109 644 86 621 86 589C86 560 110 535 139 535ZM35 387C99 379 105 374 105 307V114C105 22 103 -35 96 -78C89 -113 82 -131 70 -146C55 -162 30 -174 -1 -181C-16 -184 -23 -192 -23 -207C-23 -232 0 -253 15 -253C24 -253 33 -249 41 -242C63 -223 127 -148 162 -48C181 6 186 47 186 117V453C143 435 93 422 36 414L35 387Z" id="g58-104"></path></g></svg>. (c) Connections between nodes in the auxiliary network are activated and the auxiliary memory is retrieved. The connectivity matrix moves from state <svg height="18.1689pt" id="M23" style="vertical-align:-6.1403pt" version="1.1" viewbox="-0.0498162 -12.0286 23.1916 18.1689" width="23.1916pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.868,-3.001)"><path d="M846 629L831 655C777 615 719 595 640 595C573 595 518 604 436 619C338 640 291 647 226 647C158 647 71 626 0 558L15 532C79 570 138 592 218 592C292 592 340 582 410 569C495 552 560 540 629 540C701 540 788 559 846 629Z" id="g119-114"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z" id="g13-85"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.727,-5.741)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z" id="g50-52"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.727,3.784)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.23,3.784)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.116,3.784)"><path d="M139 535C170 535 192 560 192 589C192 621 169 644 140 644C109 644 86 621 86 589C86 560 110 535 139 535ZM35 387C99 379 105 374 105 307V114C105 22 103 -35 96 -78C89 -113 82 -131 70 -146C55 -162 30 -174 -1 -181C-16 -184 -23 -192 -23 -207C-23 -232 0 -253 15 -253C24 -253 33 -249 41 -242C63 -223 127 -148 162 -48C181 6 186 47 186 117V453C143 435 93 422 36 414L35 387Z" id="g58-104"></path></g></svg> to <svg height="18.1689pt" id="M24" style="vertical-align:-6.1403pt" version="1.1" viewbox="-0.0498162 -12.0286 23.1916 18.1689" width="23.1916pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.868,-3.001)"><path d="M846 629L831 655C777 615 719 595 640 595C573 595 518 604 436 619C338 640 291 647 226 647C158 647 71 626 0 558L15 532C79 570 138 592 218 592C292 592 340 582 410 569C495 552 560 540 629 540C701 540 788 559 846 629Z" id="g119-114"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z" id="g13-85"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.727,-5.741)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.727,3.784)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.23,3.784)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.116,3.784)"><path d="M139 535C170 535 192 560 192 589C192 621 169 644 140 644C109 644 86 621 86 589C86 560 110 535 139 535ZM35 387C99 379 105 374 105 307V114C105 22 103 -35 96 -78C89 -113 82 -131 70 -146C55 -162 30 -174 -1 -181C-16 -184 -23 -192 -23 -207C-23 -232 0 -253 15 -253C24 -253 33 -249 41 -242C63 -223 127 -148 162 -48C181 6 186 47 186 117V453C143 435 93 422 36 414L35 387Z" id="g58-104"></path></g></svg>. (d) Connections from the auxiliary to the original network are activated after original-auxiliary connections are severed. Connectivity matrix <svg height="18.1689pt" id="M25" style="vertical-align:-6.1403pt" version="1.1" viewbox="-0.0498162 -12.0286 34.4831 18.1689" width="34.4831pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,12.131,-3.001)"><path d="M846 629L831 655C777 615 719 595 640 595C573 595 518 604 436 619C338 640 291 647 226 647C158 647 71 626 0 558L15 532C79 570 138 592 218 592C292 592 340 582 410 569C495 552 560 540 629 540C701 540 788 559 846 629Z" id="g119-114"></path></g><g transform="matrix(.013,0,0,-0.013,11.263,0)"><path d="M969 650H734V615C815 608 819 591 805 531C791 472 750 316 712 193H709C654 339 597 492 541 644H493C447 490 397 339 349 197H347C313 307 279 424 246 541C232 592 233 606 308 615V650H13V615C72 607 89 593 113 515C169 337 218 169 273 -11H325C373 133 424 282 475 433H477C533 281 586 138 641 -11H693C777 269 836 443 858 508C886 591 902 605 969 615V650Z" id="g13-85"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.99,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,23.99,3.784)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path></g><g transform="matrix(.0091,0,0,-0.0091,26.492,3.784)"><path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path></g><g transform="matrix(.0091,0,0,-0.0091,31.378,3.784)"><path d="M139 535C170 535 192 560 192 589C192 621 169 644 140 644C109 644 86 621 86 589C86 560 110 535 139 535ZM35 387C99 379 105 374 105 307V114C105 22 103 -35 96 -78C89 -113 82 -131 70 -146C55 -162 30 -174 -1 -181C-16 -184 -23 -192 -23 -207C-23 -232 0 -253 15 -253C24 -253 33 -249 41 -242C63 -223 127 -148 162 -48C181 6 186 47 186 117V453C143 435 93 422 36 414L35 387Z" id="g58-104"></path></g></svg>. The original memory is retrieved.</div>

Computational and Mathematical Methods in Medicine

fig4

Figure 4

Figure 4: Preventing Neurodegenerative Memory Loss in Hopfield Neuronal Networks Using Cerebral Organoids or External Microelectronics 